Parallel Sessions Talks
Alkofer Natalia
Title: Dimensional reduction in asymptotically safe gravity
Abstract: The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. Results for the four- to five-dimensional crossover are discussed employing two forms of the background field flow. Renormalisation group trajectories allowing for a significant lowering of the true Planck scale to the electroweak scale are identified. The behaviour of the running gravitational coupling at the crossover and the true Planck scale is displayed.
Balog Ivan
Title: Understanding hysteresis
Abstract: Hysteresis related phenomena are ubiquitous in Nature. We study the random field Ising model (RFIM) as one of the simplest statistical-mechanical models that captures the anomalous irreversible collective response displayed in a wide range of physical biological and socioeconomic situations and all of the phenomenology related to hysteresis, crackling noise and avalanches. Sethna and Dahmen have elaborately demonstrated before, that understanding the collective phenomena in hysteresis lies in understanding the disorder induced phase transition seen in such systems. We have proven, by the use of the nonperturbative renormalization group (NPRG), that this non-equilibrium phase transition, is in the same universality class as the one seen in the equilibrium RFIM.
Becker Daniel
Title: Asymptotic Safety & Background Independence
Abstract: One of the fundamental assumptions a quantum theory of gravity must satisfy is Background Independence. In this talk the question is addressed whether or not this condition can be met within the framework of Asymptotic Safety, relying on the background field method. This leads to a global requirement a RG trajectory has to satisfy, i.e. originating from a non-trivial fixed point in the UV, and simultaneously restoring split-symmetry in the far IR. Employing a bi-metric Einstein-Hilbert truncation, a subset of RG trajectories fulfilling both conditions is found, whereby a running UV-attractor in the background sector turns out to be of special importance. The results further reveal an explicitly broken split-symmetry at almost every k, identifying, in particular, unreliable portions in the RG evolution of the single-metric approximation. Miraculously, the regime in the vicinity of the non-Gaussian fixed point turns out to be approximately split-symmetric and thereby surprisingly well-described by the single-metric results.
Benedetti Dario
Title: Critical behavior in spherical and hyperbolic spaces
Abstract: I will present some results on the effects of curvature on the critical behavior of scalar field theory. In particular I will concentrate on two maximally symmetric spaces, d-dimensional spheres and hyperboloids, and by making use of the local potential approximation, I will discuss the consequences of having a fixed external scale in the renormalization group equations. The talk is based on arXiv:1403.6712.
Blaizot Jean-Paul
Title: Massive renormalization scheme and perturbation theory at finite temperature
Abstract: We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.
Boettcher Igor
Title: Dimensional BCS-BEC Crossover
Abstract: We investigate how the reduction of spatial dimension influences superfluidity of ultracold two-component fermions in the BCS-BEC crossover by means of the Functional Renormalization Group. Our approach allows to study the system over the whole parameter space of interaction strength, density, temperature, spin-imbalance, and dimension. The high precision and tunability of recent experiments allows for a solid benchmarking of our description. We present results on the equation of state and the phase diagram as a function of dimension.
Brouzakis Nikos
Title: Quantum fluctuations of Galileon theories in the presence of an inhomogeneous background
Abstract: We present heat-kernel techniques in order to compute the one-loop effective action in the cubic Galileon theory for a background that realizes the Vainshtein mechanism. We find that the UV divergences are suppressed relative to the predictions of standard perturbation theory at length scales below the Vainshtein radius.
Buyukbese Tugba
Title: 1/D expansion for quantum gravity
Abstract: Large-N techniques, where N denotes the dimensions of the local gauge symmetry, are very powerful tools in the study of strongly interacting quantum fields. In gravity, the role of N is taken by the number of space-time dimensions D. We discuss the 1/D expansion for quantum gravity using functional renormalisation. We find that the theory displays an asymptotically safe UV fixed point, and that the 1/D expansion has a finite radius of convergence down to around D = 22 dimensions. Implications of the results are discussed and compared with earlier findings based on perturbation theory and effective field theory.
Christiansen Nicolai
Title: Global Flows and Vertex Functions in Quantum Gravity
Abstract: We present a novel expansion scheme for renormalization group flows in quantum gravity. We calculate the full momentum dependence of the graviton and the ghost propagator as well as the flow of the graviton three point-function. In particular, we analyze the ultraviolet fixed point and the infrared regime. For the first time, the latter shows an attractive infrared fixed point, which is smoothly connected with the ultraviolet and exhibits classical scaling of the coupling constants.
Classen Laura
Title: Instabilities on graphene's honeycomb lattice with electron-phonon interactions
Abstract: We study the impact of electron-phonon interactions on the many-body instabilities of electrons on the honeycomb lattice and their interplay with repulsive local and non-local Coulomb interactions at charge neutrality. To that end, we consider in-plane optical phonon modes with wavevectors close to the $\Gamma$ point as well as to the $K, -K$ points and calculate the effective phonon-mediated electron-electron interaction by integrating out the phonon modes. Ordering tendencies are studied by means of a momentum-resolved functional renormalization group approach allowing for an unbiased investigation of the appearing instabilities. In the case of an exclusive and supercritical phonon-mediated interaction, we find a Kekul\'e and a nematic bond ordering tendency being favored over the $s$-wave superconducting state. The competition between the different phonon-induced orderings clearly shows a repulsive interaction between phonons at small and large wavevector transfers. We further discuss the influence of phonon-mediated interactions on electronically-driven instabilities induced by onsite, nearest neighbor and next-to-nearest neighbor density-density interactions. We find an extension of the parameter regime of the spin density wave order going along with an increase of the critical scales where ordering occurs, and a suppression of competing orders.
Cuesta Raul Antonio
Title: On IR Fixed Points of Quantum Gravity
Abstract: We discuss the IR behaviour of the functional RG flow in Einstein-Hilbert gravity. We show that a singular behaviour detected previously originates from a degeneracy of fixed points. Lifting the degeneracy leads to modified RG flows including interacting and non-interacting IR fixed points with regular behaviour. Implications of our findings are discussed.
Delamotte Bertrand
Title: Derivative expansion: numerical results at order six and convergence
Abstract: We present a detailed study of the derivative expansion at order four and six of the
phi^4 model at criticality in dimensions two and three. We show in particular that while the dependence of the critical exponents on the choice of cut-off function R_k does not decrease with the order of the truncation, their values at the point of least dependence (principle of minimal sensitivity) get closer and closer to the "exact" values.
Demmel Maximilian
Title: Fixed Functionals in Quantum Einstein Gravity
Abstract: One of the current challenges in the gravitational asymptotic safety program is the transition from exploring finite-dimensional truncations to controlling RG flows of functions encoding infinitely many coupling constants. In this talk, we discuss analytical and numerical techniques to investigate the partial differential equations encoding the fixed points of asymptotic safety in the $f(R)$-truncation. In particular we outline the construction of isolated fixed functions supporting Weinberg's asymptotic safety conjecture.
D'Odorico Giulio
Title: Asymptotic freedom in projectable Horava-Lifshitz gravity
Abstract: We use the Wetterich equation on foliated spacetime to study the RG flow of projectable Horava-Lifshitz gravity coupled to Lifshitz scalars. Using novel results for anisotropic heat kernels the matter-induced beta functions for gravitational couplings in 2+1 and 3+1 dimensions are computed explicitly. We show that the RG flow exhibits an anisotropic Gaussian fixed point which is UV attractive in Newton's constant, and thus that the theory is asymptotically free. We also discuss some of the issues that the RG flow uncovers.
Eissing Katharina
Title: Functional renormalization group in Floquet space and its application to periodically driven quantum dots
Abstract: The functional renormalization group (RG) was recently extended to study interacting, low-dimensional systems out of equilibrium. This includes correlated quantum dot setups with explicitly time-dependent Hamiltonians as e.g. realized in quantum quenches or in the presence of time-dependent bias voltages [Phys. Rev. B 85, 085113 (2012), Phys. Rev. B 85, 245101 (2012)]. However, following this route periodic pumping processes, which are of particular interest in e.g. nanoelectronics and quantum information science, can only be described in an inefficient way. Taking advantage of the periodicity, we combine the Floquet theorem with the functional RG. This allows us to transform the double-time self-energy and Green functions in the Floquet basis [J.Phys.: Condens. Matter 20 085224] and the functional RG treatment resembles the stationary formalism. This makes it feasible to study transport in periodically driven systems. In my talk, I will introduce this Floquet theorem based functional RG and present first results on transport through a quantum dot described by the interacting resonant level model.
Falls Kevin
Title: UV critical behavior in quantum gravity and the cosmological constant
Abstract: We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. In the vicinity of the fixed point we find evidence that the critical exponent is given by \nu= 1/3 in agreement with lattice studies.
Fister Leonard
Title: Correlation functions in Yang-Mills theory
Abstract: We study correlation functions of Yang-Mills theory. At first, we focus on the (self-consistent) vacuum description of two-point and three-point functions, before we advance to thermal effects. In both cases, we discuss in detail the relation to first-principle studies of QCD and its phase diagram. As a direct application, we investigate the physical mechanism which is responsible for quark confinement.
Floerchinger Stefan
Title: Composite chiral fermions from the renormalization group
Abstract: The possibility that left-handed chiral fermions can be understood as composite particles consisting of right-handed fermions and scalars (or vice versa) is discussed using the functional renormalization group and a fermionic, scale-dependent, generalized Hubbard-Stratonovich transformation. The theory allows to predict Yukawa couplings as a function of the gauge couplings and a numerical calculation using the gauge interactions of the standard model suggests that leptons can indeed be seen as bound states in this sense.
Heilmann Marianne
Title: Convergence of Derivative expansion in Supersymmetric Quantum Mechanics
Abstract: We study N=1 supersymmetric quantum mechanics within the framework of the functional renormalization group (FRG). We derive the manifestly off-shell supersymmetric flow equations for the effective average action in fourth oder in the supercovariant derivative expansion. Focusing on systems with unbroken supersymmetry, we show that the energies of the first excited states nicely converge to the exactly known ones in this next-to-next-to leading order in the derivative expansion. The first excited energies are determined in a wide range of couplings including the regime where tunneling effects occur within a 1% error.
Hellwig Tobias
Title: Spontaneous breaking of SuSy in a QM system
Abstract: The spontaneous breaking of supersymmetry for a given double well potential in a quantum mechanic system will be discussed. To do so an exact flow equation in an LPA* approximation will be applied. A superfield formulation is being used and it is shown how to treat occuring auxilary fields in the SuSy broken regime. The results will be compared with those obtained by numerically diagonalizing the Hamiltonian of the system.
Henz Tobias
Title: Dilaton Quantum Gravity
Abstract: We propose a simple fixed point scenario in the renormalization flow of a scalar dilaton coupled to gravity. This would render gravity non-perturbatively renormalizable and thus constitute a viable theory of quantum gravity. On the fixed point dilatation symmetry is exact and the quantum effective action takes a very simple form. Realistic gravity with a nonzero Planck mass is obtained through a nonzero expectation value for the scalar field, constituting a spontaneous scale symmetry breaking.
Herbst Tina
Title: Sarma phase in relativistic and non-relativistic systems
Abstract: We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly- correlated systems with either relativistic or non-relativistic dispersion relation: the two-flavor quark-meson model with isospin chemical potential and ultracold atoms in the spin-imbalanced BCS-BEC crossover. The phase structures of these models look strikingly similar on the mean-field level. Using a Functional Renormalization Group approach, we now resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. While a Sarma phase at low temperatures emerges in the relativistic system, this is not the case in the non-relativistic imbalanced unitary Fermi gas. Finally, we investigate whether this conclusion remains true away from unitarity.
Huber Markus
Title: Yang-Mills correlation functions from Dyson-Schwinger equations
Abstract: Green functions are useful quantities whose applications in quantum chromodynamics range from bound state calculations to investigations of the phase diagram. Obtaining them from functional equations faces the challenge of devising a proper truncation scheme. I will report on recent progress to determine the correlation functions of pure QCD from Dyson-Schwinger equations in the vacuum and at non-zero temperature. Results for two-, three- and four-point functions were obtained that hint at favorable convergence properties of the system. This helps to establish functional equations as a first principles method in QCD.
Itoh Katsumi
Title: Functional RG and a solution to the modified WT identity for QED
Abstract: Within the framework of Functional Renormalization Group, we discuss how gauge symmetry is realized in QED. The modified Ward-Takahashi identity (mWT id.) for the Wilson action contains a non-trivial loop contribution as a Jacobian factor from the functional measure. We extract two relations (WT relations) out of the mWT id. which require the presence of a momentum dependent (non-local) mass-like term as well as higher dimensional interactions in the Wilson action. We solve these relations exactly and obtain a gauge invariant Wilson action, by introducing form factors in the chiral invariant 4-fermi couplings. Taking account of momentum dependence in the WT relations, we obtain the condition corresponding to the standard Z_{1} = Z_{2} as well as a relation among 4-fermi couplings, that gives the momentum dependence of the couplings. Properties of the solution will be discussed.
Jakovac Antal
Title: Effective action for fermion composite operators
Abstract: The evolution of the effective action of purely fermionic interacting systems will be discussed in the talk. It will be shown that, below some compositeness scale, the effective potential can be a general function of fermionic invariants. As concrete examples we will discuss the evolution equation of the Gross-Neveu and Nambu-Jona-Lasinio models, and in case of the Gross-Neveu model the wave function renormalization constant and the fixed point potential will also be shown.
Janssen Lukas
Title: Quantum critical points on graphene's honeycomb lattice
Abstract: The nature of the quantum phase transitions on graphene's honeycomb lattice has been under much debate. Recently, the results began to converge towards the scenario with
direct and continuous transitions between the semimetallic and Mott-insulating states. The characterization of these transitions on a quantitative level, however, has just begun. I will discuss the effective Gross-Neveu Yukawa models that describe the transition into the charge density wave and the antiferromagnetic state, respectively. The former is expected for large nearest-neighbour interaction on the honeycomb lattice, and its critical point is fairly well understood. By contrast, the latter, which is expected for large on-site repulsion, has so far much less been studied. As the universal exponents are currently also aimed at in simulations, a detailed comparison between different competing approaches to the problem will be possible in the future, and I will confront the latest Monte Carlo predictions with our FRG results. I will also show that the universality classes considered provide an ideal testing ground to investigate the validity of nonperturbative approximation schemes within the FRG and beyond.
Reference: L. Janssen and I. F. Herbut, Phys. Rev. B 89, 205403 (2014).
Juricic Ana
Title: Probing the QCD Phase Diagram with Generalized Quark Susceptibilities
Abstract: A distinctive feature of QCD phase diagram is a possible critical end point, which is hard to detect experimentally due to finite volume and critical slowing down effects. Promising candidates for its characterization are higher moments of particle distributions which depend on higher powers of the correlation length, and thus are more sensitive to criticality. The effect of quantum and thermal fluctuations of these quantities in the phase diagram are addressed within the FRG in a quark-meson model truncation and compared to mean-field approximations where the meson fluctuations are ignored.
Kamikado Kazuhiko
Title: Magnetic susceptibility of the strongly interacting matter
Abstract: Properties of the strongly interacting matter in external magnetic field has received much attention. We investigate chiral phase transition and thermodynamics of the strongly interaction matter with a presence of the external magnetic field. The functional renormalization group equation is utilised to incorporate neutral and charged meson fluctuations in addition to quark contributions. We find, in the hadron phase, the matter is diamagnetic due to light charged mesons. On the other hand, in the quark gluon phase, quark contributions become domination and the matter shows paramagnetic behaviour. We confirm near the pseudo-critical temperature, the matter becomes diamagnetic to paramagnetic with increasing temperature. We also analyse magnetic field dependence of the chiral critical temperature.
Khan Naseemuddin
Title: The role of fluctuations in the QCD phase diagram
Abstract: We construct an effective quark meson diquark model to simulate QCD at low energies. We employ the framework of the functional renormalization group, within which fluctuations of fermions and bosons can be included. We study the behavior of the chiral condensate at various temperatures and chemical potentials as well as the diquark condensate, which arises at higher chemical potentials.
Kloss Thomas
Title: Kardar-Parisi-Zhang growth with spatially correlated noise
Abstract: To describe interface roughening and dynamical scaling, Kardar, Parisi and Zhang (KPZ) proposed a nonlinear Langevin equation, which has now emerged as a fundamental model for nonequilibrium phase transitions and scaling phenomena. Despite its apparent simplicity, the KPZ equation has resisted most of the theoretical attempts to provide a complete description of its strong-coupling phase in generic dimensions, which requires nonperturbative methods. In the present study we investigate a variant of the KPZ equation including spatially long-range correlated noise. Analyzing the RG flow and the stability of the fixed-point solutions in various dimensions allows us to probe the phase diagram including the strong-coupling sector. Our findings lead to a unified picture that is both consistent with exact results valid at weak coupling as well as lattice simulations in the strong-coupling regime.
Kobayashi Tamao
Title: Domain Wall Renormalization Group Approach to the 2d Ising Model
Abstract: We represent the spin configuration of 2-dimensional Ising model by the domain wall configuration defined on the dual link and formulate the domain wall renormalization group (DWRG) according to the tensor network renormalization technique. DWRG realizes the idea of coarse graining of domain walls and gives an advantage which we can get the clear physical picture as a renormalization group. We show DWRG is extended to include the external magnetic field and its eigenvalues around the non-trivial fixed point is calculated to give the magnetic susceptibility exponent.
Kopietz Peter
Title: Solution of the Anderson impurity model via the functional renormalization group
Abstract: We show that the functional renormalization group is a numerically cheap alternative to Wilson's numerical renormalization group to obtain the low-energy behavior of the Anderson impurity model describing a localized interacting electron coupled to a bath of conduction electrons. Our approach uses an external magnetic field as flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices which are fixed by Ward identities. We calculate the quasi-particle residue and the spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with exact Bethe-ansatz results for arbitray interaction.
Kumamoto Shin-Ichiro
Title: Weak Renormalization Group Analysis of the Dynamical Chiral Symmetry Breaking
Abstract: We analyze the spontaneous chiral symmetry breaking in the Nambu-Jona-Lasinio model by solving non-perturbative renormalization group equation. The equation is a nonlinear partial differential equation (PDE), and the target function is the multi-fermion effective interactions $V(x,t)$, where x is the bilinear fermion operator and $t$ is the logarithm of the renormalization scale. In case that the spontaneous chiral symmetry breaking occurs, the nonlinear PDE encounters some non-analytic singularities at the finite critical scale even though the initial function is continuous and smooth. Therefore there is no usual solution of the PDE beyond the critical scale. We introduce the notion of a weak solution to get the global solution including the infrared limit and show its properties. The obtained weak solution perfectly describes the physically correct vacuum even in the case of the first order phase transition appearing in a finite-density medium, which is also demonstrated by the auto-convexification of the effective potential. In collaboration with Ken-Ichi Aoki (Kanazawa U.) and Daisuke Sato (Kanazawa U.)
Lammers Soren
Title: Momentum distribution of ultracold bosons in two and three dimensions
Abstract: Experiments with ultracold atoms are able to probe systems consisting of bosons or molecules over a wide range of parameters, like temperature, density and interaction strength. In particular it is possible to measure the momentum distribution during a time-of-flight expansion after the gas is released from the trap. The momentum distribution constitutes a key observable to characterise the state of the quantum many-body system. Its computation for strong coupling requires non-perturbative techniques. We present results on the momentum distribution of ultracold bosons in two and three dimensions from Functional Renormalization, and compare them to experiments.
Lippoldt Stefan
Title: Fermions in gravity with local spin-base invariance
Abstract: We study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin-base transformations. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vierbein field is not required. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions.
Litim Daniel
Title: Do interacting UV fixed points exist fundamentally, and if so, what can we do with them?
Abstract: It is widely acknowledged that the high-energy behaviour of QFTs should be controlled by ultraviolet fixed points. The fascinating idea that such fixed points could be interacting has triggered substantial research in recent years, both in particle physics and gravity. I discuss how perturbatively controlled interacting UV fixed points arise in models of particle physics involving gluons, fermions, and scalars. The origin of asymptotic safety is explained, including the phase diagram and extensions towards strong coupling and applications in gravity.
Luecker Jan
Title: Polyakov-loop potential from functional methods
Abstract: In model studies of the QCD phase diagram the Polyakov-loop potential is an important input, which is usually modelled along lattice results. In my talk I will present a calculation of the Polyakov-loop potential based on QCD propagators. To this end, a combination of Dyson-Schwinger and FRG equations for the quark, gluon and ghost propagators is used. This allows to take effects of unquenching and finite baryon density into account. I will compare to popular model potentials and show results from the Polyakov-loop extended quark meson model as an application. Furthermore, I will consider the limit of heavy quarks, where the deconfinement transition changes from crossover to first order. In this regime it is possible to compare to lattice results also at finite chemical potential.
Maier Stefan
Title: Fermionic functional renormalization group approach to phases with simultaneous breaking of discrete and continuous symmetry
Abstract: We present a channel-decomposed functional renormalization group formalism for interacting fermions on lattices that captures the flow into states with commensurate antiferromagnetic order. The simultaneous breaking of the translational and SU(2) symmetries gives rise to a plethora of effective interaction terms. In order to reduce the computational effort, we propose an approximate parametrization, which captures the physics of the Goldstone theorem and reproduces the mean-field gap equation exactly in random-phase approximation. We use the corresponding Ward identity to check the accuracy of the results, and apply our method to a model with two Fermi pockets that have perfect particle-hole nesting. Finally, an extension of the formalism to the case of possibly coexisting antiferromagnetic and superconducting orders will be given.
[1] Stefan A. Maier, Andreas Eberlein, Carsten Honerkamp, arXiv:1406.2906
Mao Shijun
Title: Functional Renormalization for Deconfinement Phase Transition in Friedberg-Lee Model
Abstract: We investigate the deconfinement phase transition at high temperature and density in the frame of Friedberg-Lee model. The method we employ is based on the exact renormalization group equation for the free energy. The truncated nonperturbative flow equations are derived and solved via both grid and potential expansion. We find that the deconfinement is a first order phase transition at high temperature and density.
Marchais Edouard
Title: Fixed points of critical scalar field theories
Abstract: We are using the functional renormalization group at leading order of the derivative expansion to investigate the fixed point structure of O(N) symmetric scalar field theories. At infinite N, global UV and IR fixed points are found analytically. At finite N, the radius of convergence of polynomial expansions is bound by singularities in the complex field plane. Reliable results for physical observables are obtained by combining numerical and analytical methods. Implications beyond the leading order of the derivative expansion, and for other theories, are discussed.
Mathey Steven
Title: Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence
Abstract: Anomalous scaling at non-thermal fixed points is investigated by means of functional renormalization group equations. We focus on scaling solutions found at renormalization group fixed points of the stochastic driven dissipative Burgers equation. Relations to Kardar-Parisi-Zhang scaling solutions and Gross-Pitaevskii turbulence are discussed. A scaling analysis allows for a new renormalization-group fixed point which is expected to play a role in the case of forcing non-local in space. Moreover, using average literature values for anomalous exponents we relate the present study to strong-wave-turbulence analyses of non-thermal fixed points of Gross-Pitaevskii systems. This allows us to infer anomalous scaling at non-thermal fixed points related, in position space, with sound wave turbulence. Our predictions can be experimentally investigated in, e.g., exciton-polariton condensates in solid-state systems, or in ultra cold atomic gases.
Mati Peter
Title: The 3d O(N) model in the large N limit
Abstract: I will show how the effective potential of the O(N) model can be obtained using FRG methods. For the large N case an analytical solution is provided. There will be a comparison between the polynomial approximation and the analytical solution, showing differences in the fixed point structure of the theory. The corresponding critical exponents will be extracted by the eigenperturbation technique.
Meurice Yannick
Title: The Tensor Renormalization Group approach of lattice models: from exact blocking formulas to numerical results
Abstract: We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and SU(2)) on (hyper) cubic lattices in order to obtain exact and compact blocking formulas. The formulation separates neatly the degrees of freedom inside the block and which are integrated over, from those kept to communicate with the neighboring blocks. Controllable numerical truncations permit to handle large volumes and to get rid of some sign problems. We present numerical results regarding the critical properties of the 2D O(2) nonlinear sigma model with complex beta and chemical potential and their relationship with Bose-Hubbard models. We discuss recent results concerning the search of fixed points, gauge fixing procedures, Grassmann variables and the introduction of quenched disorder.
Missarov Mukadas
Title: Exactly solvable renormalization group model and new conjectures in general renormalization group theory
Abstract: We consider four-component fermionic (Grassmann-valued) field on the hierarchical lattice. The Gaussian part of the Hamiltonian in the fermionic hierarchical model is invariant under the block-spin renormalization group (RG) transformation with some fixed degree of normalization factor (RG parameter). The non-Gaussian part of the Hamiltonian is given by the self-interaction forms of the 2-nd and 4-th order. The action of the block-spin RG transformation in the fermionic hierarchical model is reduced to the rational map in the plane of coupling constants. Using the projective space representation we give explicit description of the global RG-flow in the whole plane of the coupling constants and all values of RG parameter. The exact solution of the fermionic hierarchical model reveals symmetry and dynamical properties of renormalization group transformation which cannot be found by perturbation theory methods. Fermionic hierarchical model has natural continuous version and can be described in terms of the quantum field theory approach and Wilson’s renormalization group. Ultraviolet poles and renormalization procedure have a nice interpretation in terms of classical mathematics. Formal descriptions and epsilon-expansions for critical exponents show strong algebraic similarity between hierarchical and Euclidean models. The exact solution of the fermionic hierarchical model generates a list of non-trivial mathematical and physical conjectures for the different fermionic and bosonic hierarchical and Euclidean field models.
Mitter Mario
Title: QCD and dynamical hadronization
Abstract: We present an analysis of chiral symmetry breaking in two-flavour quenched QCD. The theory is set-up at a scales of the order of 10-100 GeV, where asymptotic freedom gives quantitative precision within perturbation theory. The evolution of QCD towards the hadronic phase is computed with the sole input of the quenched gluonic two-point correlation, employing dynamical hadronisation. We discuss the quantitative convergence of the present approximation scheme and the remaining systematic errors. Results for the quark propagator, the quark-gluon vertex, as well as dynamically created four-fermion interactions are provided. The role of mesonic fluctuations and the details of the mechanism of chiral symmetry breaking are discussed.
Moroz Sergej
Title: Super Efimov effect for mass imbalanced systems
Abstract: Following the talk of Yusuke Nishida, I will present our recent study of a two-dimensional three-body quantum problem fine-tuned to a p-wave resonance. The system consists of two particles of one species and one of the other. Using renormalization group equations it will be shown to exhibit the super Efimov effect above the critical mass ratio. With increasing the mass imbalance, the super Efimov spectrum becomes denser which would make its experimental observation easier. I will also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect in this system.
Mueller Niklas
Title: Magnetic Fields from Flow Equations
Abstract: Extreme magnetic fields in non central heavy ion collision are expected to modify the behavior of matter dramatically. Although the importance after the system thermalized is still under debate, the influence during the early stages of a collision is certainly essential. Aside from this magnetic fields play an important role for quantum systems in a variety of other cases,for example in cosmology. We employ the Ritus method to include the interaction of a quantum system with external Abelian fields to all orders. Similar as with temperature and chemical potential, magnetic fields are an infrared effect, a fact that makes the functional renormalization group an excellent tool for their investigation. We present how a "magnetic flow" can be constructed, which, similar to thermal flows, includes only the "magnetic" fluctuations as one goes along the flow trajectory from the UV towards the full theory in the IR. Further we will use propagators obtained in this way to investigate the beta function of the four fermion coupling, which is modified in the presence of a magnetic field and discuss its implication on chiral symmetry in QCD.
Nagy Sandor
Title: Critical exponents in quantum Einstein gravity
Abstract: The quantum Einstein gravity is treated by the functional renormalization group method using the Einstein-Hilbert action. The ultraviolet non-Gaussian fixed point is determined and its corresponding exponent of the correlation length is calculated for a wide range of regulators. It is shown that the exponent provides a minimal sensitivity to the parameters of the regulator which correspond to the Litim's regulator. It is also shown that in d=4 the exponent is exactly 1/2 in the vicinity of the gaussian and the infrared fixed points. However the anomalous dimension has different scaling behavior in the ultraviolet, crossover and infrared scaling regimes.
Nandori Istvan
Title: The Compactly Supported Smooth Regulator
Abstract: A new type of regulator function, i.e. the compactly supported smooth (CSS) regulator is introduced. It can be considered as a prototype regulator because it reduces to all the major types of regulator functions (exponential, power-law, Litim) in appropriate limits of its parameters. Thus, it can be used to compare various regulator functions to each other in the framework of the Principle of Minimal Sensitivity optimization scenario. Furthermore, it has derivatives of all orders with a compact support, so it can be applied to consider the Litim-limit at any order of the gradient expansion which represents an approximate solution for the Litim-Pawlowski optimization conditions. Considerations are done for three different models, in three different dimensions at various orders of the derivative expansion (in LPA and beyond) with various optimization methods and all these results indicate that the Litim-limit of the CSS is the most favorable choice.
Pawlowski Jan M.
Title: FRG-QCD: status and prospects
Abstract: In this talk I summarise the results obtained within the FRG-QCD collaboration (J. Braun, L. Fister, T. Herbst, M. Mitter, JMP, N. Strodthoff, F. Rennecke, see also related talks) for full dynamical QCD with an emphasis on quantitative aspects as well as the interplay between chiral symmetry breaking and confinement.
Platt Christian
Title: Functional RG in Multi-Orbital Systems
Abstract: Technological progress in material synthesis, as well as artifical realization of condensed matter scenarios via ultra-cold atomic gases or epitaxial growth of thin films, is opening the gate to investigate a plethora of unprecedented strongly correlated electron systems. In a large subclass thereof, the multi-orbital characteristic of the underlying electronic structure decisively influences the corresponding ground-state properties. In this talk, I will present functional RG studies of two such multi-orbital systems (Sr2RuO4 & NaxCoO2) and discuss the emergence of topological pairing states therein.
Rachwal Leslaw
Title: Super-renormalizable & Finite Gravitational Theories
Abstract: We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite too. Therefore we have the possibility for "finite quantum gravity" in any dimension.
Rechenberger Stefan
Title: Chiral Dynamics in External Magnetic Fields
Abstract: Very strong magnetic fields are expected to be relevant for non-central heavy-ion collisions. Therefore the study of the phase diagram of the theory of the strong interaction under the consideration of strong external magnetic fields is a very active area of research. In order to better understand discrepancies between predictions for, e.g., the critical temperature of the chiral phase transition from first-principles lattice studies and calculations based on low-energy models of Quantum Chromodynamics (QCD), we are analyzing the chiral dynamics in the presence of an external magnetic field by discussing the fixed-point structure of QCD, with an emphasis on the finite-temperature phase boundary.
Reckling Timo
Title: Correlated electrons in the Hubbard Model on the Bilayer Square Lattice
Abstract: We study the Hubbard model on the bilayer square lattice at and away from half-filling as a model unifying various aspects of the physics of two-dimensional correlated fermions. We discuss the model with pure onsite interaction by means of an unbiased functional renormalization group approach. This allows us to deduce the emergent order without previous assumptions about its nature and symmetry and therefore can be used to establish the appearence of antiferromagnetic ordering. As an independent complement to our study, we add determinantal quantum Monte Carlo simulations from collaborators and discuss their results in relation to our method. We then move away from half-filling and further include interlayer interactions, which drives superconducting and charge density ordering tendencies. Thus we obtain a comprehensive picture of this model for the whole range of onsite interactions at half-filling and a tentative leading instability diagram away from half-filling.
Rennecke Fabian
Title: The Chiral Phase Transition of QCD from the Functional Renormalization Group
Abstract: There are still many open questions on the phase structure of QCD. While lattice gauge theory provides results on the phase diagram at vanishing density from first principles, the notorious sign problem is not yet circumvented and thus only very little is known about the QCD phase diagram at finite density. Functional continuum methods, on the other hand, do not suffer from technical difficulties at finite density, but have to rely on truncations of the full effective action and can therefore be viewed as complementary to the lattice approach. We will show how the perturbative high-energy regime of QCD is dynamically connected to the low energy sector by renormalization group flows. This way, a connection between first-principle QCD and effective low energy models is established. Then, we will present results on the chiral phase boundary of two-flavor QCD within an effective quark-meson model. We will discuss the impact of higher order meson-meson and quark-meson interactions on the phase structure and the influence of fluctuations on the location of the critical endpoint.
Roscher Dietrich
Title: Phases of unitary imbalanced Fermi gases
Abstract: Ultracold Fermi Gases have attracted a lot of attention in the past 15 years, as they provide an accessible and clean environment to study quantum many body phenomena from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity (BCS). While experimentally well accessible, the theoretical description of the "unitary" limit of large s-wave scattering length, corresponding to a strongly coupled regime, is particularly challenging due to the lack of an obvious small expansion parameter. Additional complications arise, if a population and/or mass imbalance between the components of the gas is introduced. In order to gain insight into the properties of these systems, a functional RG formalism, which has been developed for the description of balanced Fermi gases in the BCS-BEC crossover region, is extended to include such imbalances. The resulting phase structure will be discussed, addressing questions such as the nature of the phase transitions, the existence of a critical point and the extent of the superfluid phase beyond the mean field approximation.
Saltas Ippocratis
Title: Classical and quantum aspects of unimodular gravity
Abstract: In this talk, I will discuss the classical and quantum dynamics of unimodular gravity, based on a unimodular formulation of GR which enjoys full diffeomorphism symmetry by construction. I will first explain how the classical dynamics of the theory are exactly those of standard GR, and how the cosmological constant problem expresses itself in this context. I will proceed with presenting the key quantum properties of the theory in the context of the Exact Renormalisation Group and compare with those of GR, explaining how (in)equivalence between the two theories in the UV is established.
Satz Alejandro
Title: Asymptotic safety and limit cycles in minisuperspace quantum gravity
Abstract: We derive renormalization group equations for quantum gravity in an effective symmetry-reduced approximation. The Euclidean minisuperspace theory is covered as a particular value of a model parameter, n. The RG flow displays ultraviolet and infrared fixed points, but the availability of an asymptotic safety scenario depends on the value of n. For most values, the fixed points are connected by asymptotically safe trajectories, similar to those of the Einstein-Hilbert theory. In a certain parameter range including the minisuperspace theory, we detect an infrared limit cycle which shields asymptotic safety. For a critical value of n, we also detect an asymptotically safe, but degenerate, limit cycle. This novel scenario predicts a small cosmological constant at low energies for all trajectories emanating from the ultraviolet fixed point.
Saueressig Frank
Title: Universality classes of Quantum Gravity
Abstract: Horava-Lifshitz gravity is a proposal for constructing a perturbatively renormalizable quantum theory for gravity by relaxing the symmetry principles of general relativity to foliation preserving diffeomorphisms. The setting introduces an anisotropic scaling between Euclidean space and time-directions which makes the theory power-counting renormalizable. In this talk, we discuss the new RG fixed points that appear in this generalized setting and outline the perspectives that they may provide a valid UV completion of gravity. Their relation to the non-Gaussian fixed point underlying the gravitational Asymptotic Safety program will be discussed in detail.
Scherer Daniel
Title: Unconvetional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
Abstract: The Kitaev-Heisenberg model on the honeycomb lattice can describe the magnetic ground-state of the spin-orbit Mott insulator Na2IrO3. I will present our analysis of the quantum many-body instabilities found in the doped system within the framework of a t-J model. We determined the leading ordering tendencies by the functional renormalization group (fRG) method for correlated fermion systems. To this end, we derived fRG flow-equations and Ward identities adapted to the lack of full spin-rotational invariance in the fermionic interactions caused by the highly anisotropic and frustrated Kitaev exchange. The solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold (quantum spin liquids, magnetically ordered phases) of the Kitaev-Heisenberg Hamiltonian. We confirm superconducting p-wave instabilities driven by ferromagnetic exchange, and find unconventional bond-order states supported by Fermi-surface nesting.
Schober Giulio
Title: Interaction effects in Rashba-type tight-binding models from the functional renormalization group
Abstract: We investigate the interplay between spin-orbit coupling and electron-electron interaction using the functional renormalization group. Our aim is an unbiased theoretical description of the low-energy properties of BiTeI, a semiconductor with giant bulk Rashba-type spin splitting. Starting from an effective tight-binding model for the spin-split lowest conduction bands, we successively integrate out the high-energy degrees of freedom to study the competition between different Fermi liquid instabilities. We focus on unconventional superconducting states which may arise in the absence of spin SU(2) symmetry. The flow of effective interactions is realized in an N-patch scheme which takes into account the most relevant momenta on the Fermi surface and the full spin dependence of the four-point vertex. Abstracting from the concrete material, we further study a class of minimal tight-binding models on the hexagonal Bravais lattice with Rashba-type dispersion near several time-reversal invariant momenta in the first Brioullin zone.
Schroeder Jan
Title: Asymptotic Safety and Matter
Abstract: We provide further insights into the implications of matter corrections to the asymptotic safety scenario. In 4D we go beyond the Einstein Hilbert approximation and study the effects of higher scalar invarinats in R for scalar, fermionic and vector matter.
Shinnosuke Onai
Title: Analysis of the Spontaneous Mass Generation by Using an Iterative Method
Abstract: A new iterative method is developed to analyze the spontaneous mass generation due to the dynamical chiral symmetry breaking in the Nambu-Jona-Lasinio model and in the gauge theory. The dynamical chiral symmetry breaking occurs by summing up the infinite number of Feynman diagrams defined on the perturbative vacuum. We define an iterative transformation, which sums diagrams up to a definite ``length" or ``depth". The infinite number of iteration leads us to an attractive fixed point, which gives the finite mass generated by the infinite number of diagrams. We demonstrate that above the critical coupling constant, there actually exits a non-trivial attractor which does not vanish as far as we take the zero bare mass limit at last. Our procedure reveals how the perturbatively massless particle gains the finite mass spontaneously. This method can be regarded as a new regularization of the singular mass function or the fermion potential function appearing in the dynamical chiral symmetry breaking.
In collaboration with Ken-Ichi Aoki (Kanazawa U.) and Daisuke Sato (Kanazawa U.)
Sondenheimer Rene
Title: Higgs mass bounds from the functional renormalization group
Abstract: We investigate various Higgs-Yukawa models to mimic the Higgs sector of the standard model within the framework of the functional renormalization group. For the class of standard bare potentials of \phi^4-type at a given ultraviolet cut-off, we show that a finite infrared Higgs mass range emerges naturally from the renormalization group flow itself. By contrast, more general bare potentials allow to diminish the lower bound considerably. We identify a simple renormalization group mechanism for this depletion of the lower bound. If active also in the full standard model, Higgs masses smaller than the conventional infrared window do not necessarily require new physics at low scales or give rise to instability problems.
Sonoda Hidenori
Title: On the universality of critical exponents
Abstract: A general ERG differential equation is characterized by two functions of momenta: one for partial integration over field fluctuations and the other for field rescaling. For example, the differential equation of Wilson and that of Polchinski correspond to different choices of these functions. Given a fixed point of the ERG differential equation, I will show that the scale dimensions of composite operators defined at the fixed point do not depend on the choice of the two functions of momenta.
Springer Paul
Title: Dynamical locking of the chiral and the deconfinement phase transition in QCD at finite chemical and isospin chemical potential
Abstract: Studies of the QCD phase diagram at finite temperature and quark chemical potential are currently one of the most discussed topics in theoretical physics and are of great importance to better our understanding of heavy-ion collision experiments. However, the relation of confining and chiral dynamics is not yet completely understood. At vanishing chemical potential, results from lattice QCD indicate that the chiral and the deconfinement phase transition lie close to each other. In this talk, we analyze the fixed-point structure of four-fermion interactions in two-flavor QCD and show that there indeed appears to be a mechanism which dynamically locks the chiral phase transition to the deconfinement phase transition, both at vanishing and at finite quark chemical potential. As a direct consequence, this observation suggests that the chiral phase transition to the deconfinement phase transition temperatures lie close to each other, at least for small quark chemical potentials.
Toschi Alessandro
Title: From Infinite to Two Dimensions through the Functional Renormalization Group
Abstract: We present a novel scheme [1] for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, our method -coined DMF2RG - allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account non-perturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling.
[1] C. Taranto, S. Andergassen, J. Bauer, K. Held, A. Katanin, W. Metzner, G. Rohringer, and A. Toschi, Phys. Rev. Lett. 112, 196402 (2014).
Trombettoni Andrea
Title: Volume Law for the Entanglement Entropy in presence of Long-Range Interactions
Abstract: We show how a violation of the area law for the entanglement entropy may emerge in fermionic lattices, and investigate when a volume law is obtained. We first consider long-range couplings with power-law exponent, showing that it is not (only) the long-range-ness that matters, but rather the topology of the Fermi surface: as a (pathological) example of this situation we consider the fully connected lattice. Motivated by these results, we present a constructive theorem exhibiting explicitly the general form of the states rendering the entanglement entropy S maximal, i.e. linear in the size L^d of the subsystem. For translational invariant one-dimensional systems these states are obtained at half-filling occupying, according to the Fermi statistics, all even (or odd) wavevectors, corresponding to a "zigzag" alternate Fermi surface in momentum space. Other examples of one-dimensional systems displaying deviations from area law are proposed and discussed.
Tsuchiizu Masahisa
Title: Spin Triplet Superconductivity in Sr_{2}RuO_{4} due to Orbital and Spin Fluctuations
Abstract: In order clarify the mechanism of the triplet superconductivity in Sr_2RuO_4, we study the (d_{xz}, d_{yz}) multi-orbital Hubbard model by applying the renormalization-group method combined with the constrained random phase approximation, which we call the RG+cRPA method [1]. From the naive RPA calculation, it is known that the spin fluctuation develops and the spin-singlet superconductivity is obtained due to the conventional spin-fluctuation mediated pairing interaction. By taking into account vertex corrections, we find that the strong orbital and spin fluctuations emerge and the spin-triplet superconductivity is obtained due to the cooperation of both fluctuations. We also give the arguments on the relevant vertex correction for the enhancement of the orbital fluctuation.
[1] M. Tsuchiizu et al., Phys. Rev. Lett. 111, 057003 (2013).
[2] M. Tsuchiizu et al., arXiv:1405.2028.
Vacca Gian Paolo
Title: LPA in an ERG analysis for a simple scalar-fermions system
Abstract: We explore some consequences of generalizing a simple trilinear Yukawa scalar-fermion interaction to a truncation with a term dependent on a generic function of the scalar field together with a self-interacting scalar potential.
Wentzell Nils
Title: Non-perturbative starting point for the functional renormalization group
Abstract: We present a general frame to extend fRG-based approximation schemes by using an exactly solvable reference solution as starting point for the flow. This allows for a systematic expansion around an interacting reference system where correlation effects are accounted for in a non-perturbative way. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. We establish a connection to the recently introduced DMF$^2$RG, which includes the dynamical mean-field theory (DMFT) solution as starting point of the fRG flow, and comment on the relation to the dual fermion formalism. We finally discuss the potential for future applications.
Wetterich Christof
Title: Dilaton quantum gravity and cosmology
Abstract: I will connect the crossover between an UV and IR fixed point with the different epochs of the cosmological evolution, with one single scalar field describing inflation and dynamical dark energy.
Wetzel Sebastian
Title: Competing orders and multicritical phenomena
Abstract: We discuss the phase structure of models with two competing order parameters. We examine the nature of multi critical points, where lines of phase transitions meet. In our model there exist several fixed points. Their stability depends on the choice of the symmetry groups of each order parameter.
Wipf Andreas
Title: Asymptotic Safety of Nonlinear O(N)-Models
Abstract: Quantum Field Theories which are non-renormalizable in perturbation theory may be renormalizable beyond perturbation theory. Examples are 4-Fermi theories and nonlinear sigma models in 3 spacetime dimensions and quantum gravity. I shall present and compare results on the realization of the asymptotic safety scenario for nonlinear O(N)-models as obtained with the renormalization group equation in the continuum and the corresponding lattice models with simulations.
Yamada Masatoshi
Title: A beyond the local potential approximation study for the dynamical chiral symmetry breaking in effective model of QCD
Abstract: We study the 2-flavor and 3-color quark-meson model as a chiral effective model of QCD at finite temperature and finite density. We set up the functional renormalization group equation including the effects of the anomalous dimensions and the running Yukawa coupling constant, which are both functions of the meson fields. We solve the RG equations, coupled partial differential equations, and discuss the behaviors of the RG flows and resultant chiral phase structures.
Zambelli Luca
Title: Higher-spins, momenta expansion, and the functional RG
Abstract: An exact renormalization group equation for Wilson's effective action is translated, by means of a generalized Hamiltonian formalism, into an equation for an effective Hamiltonian density that depends on configuration variables and on momenta fields with higher spins. Neglecting the spacetime-dependence of the couplings parameterizing such a Hamiltonian, one can reduce the RG equation to a partial differential equation for a function of infinitely-many fields. A natural approximation scheme in this framework is the expansion of the Hamiltonian in momenta fields, which might be considered as an alternative to the usual derivative expansion. We describe this construction in the simple case of a scalar field theory and we apply it to the study of its critical behavior, in order to test and compare the new method and approximations to known results.