Plenary Speakers
Berges Jürgen
Title: Universality far from equilibrium: From superfluid Bose gases to heavy-ion collisions Abstract: TBA
Canet Leonie
Title: Fully developed isotropic turbulence from Navier-Stokes equations
Abstract: I will present the general functional renormalization group formalism to study the regime of fully developed turbulence of the Navier-Stokes (NS) equation with stochastic forcing for incompressible fluids. I will review the derivation of a field theory from this equation and analyze in details its symmetries, showing in particular that they admit gauged forms. I will then present the NPRG flow equations at the Leading Order approximation, and their numerical integration. I will show that they lead to a fixed point solution in two and three spatial dimensions, and calculate the associated two-point structure function and energy spectrum within this approximation. However, I will explain how this fixed point does not entail the usual scale invariance, because of the absence of a regular limit when the integral scale (the typical length scale of energy injection) tends to infinity. To demonstrate this, I will derive exact NPRG flow equations in this limit, and show how violations of the naive Kolmogorov scaling can emerge.
Codello Alessandro
Title: ERG and Weyl invariance
Abstract: RG flows can be described quite well around a given fixed point, where linearized RG transformations, or more generally CFT data, is sufficient to describe its properties accurately. But away from criticality the RG flow is generally more evasive, since perturbative expansions generally become useless. To date there are basically only two general analytical techniques able to tackle with the global properties of RG flows: exact RG equations and Weyl consistency conditions. While the first allows for the explicit construction of the flow in every point of theory space, the second leads to constraints on the flow, and ultimately to the definition of the c-- and a--functions. In the talk I will briefly describe these two approaches and then I will try to explain how to construct a bridge between the two.
Diehl Sebastian
Title: Dynamical Criticality in Driven Open Quantum Systems
Abstract: Quantum optics and many-body physics increasingly merge together in ultracold atomic gases and certain classes of solid state systems. This gives rise to new non-equilibrium scenarios in stationary state, where coherent and dissipative dynamics appear on an equal footing. Here we report on dynamical critical phenomena of the non-equilibrium Bose condensation transition in many-body ensembles subject to particle loss and pumping, as realized in exciton-polariton systems in semiconductor hetetostructures. Using both functional and perturbative field theoretical renormalization group approaches, in three spatial dimensions we establish an effective thermalization mechanism of the low frequency dynamics. Still, the microscopic drive conditions are witnessed even on the largest scales via a new, independent universal critical exponent. Such systems thus define an out-of equilibrium universality class beyond the classification scheme of equilibrium dynamical transitions. The markovian noise level generically present in such systems provides a non-equilibrium analog of classical critical behavior. Using functional renormalization, we furthermore analyze a scenario of non-equilibrium driven quantum criticality in one-dimensional systems, which is motivated by recent developments in the context of coupled microcavity arrays.
Eberlein Andreas
Title: Spontaneous symmetry breaking in interacting fermion systems II: Purely fermionic formalism
Abstract: Spontaneous symmetry breaking is a ubiquitous phenomenon in many branches of physics. In solids, spontaneous symmetry breaking is often caused by interactions between electrons, that is, fermions. In our lecture we review how spontaneous symmetry breaking in interacting fermion systems can be treated by the functional renormalization group. There are two distinct ways of implementing spontaneous symmetry breaking in fermion systems. One approach is a purely fermionic flow with an order parameter leading to anomalous propagators and interaction vertices. Another possibility is to decouple the two-fermion interaction by a bosonic order parameter field, via a Hubbard-Stratonovich transformation, and to compute the coupled flow involving fermions and order parameter fields. We discuss both approaches, using U(1) symmetry breaking in fermionic superfluids as a prototypical example for the case of a broken continuous symmetry with an emergent Goldstone mode.
Eichhorn Astrid
Title: Probing phase transitions between discrete and continuum quantum spacetime
Abstract: I will review the matrix- and tensor-model approach to quantum gravity, which is based on discrete building blocks for quantum spacetime. The main open question in this approach is whether a continuum limit can be found, in which an extended spacetime emerges from the discrete building blocks. I will discuss the Functional Renormalization Group as a novel tool to tackle this question. In particular, I will show how to set a scale in discrete approaches to quantum gravity, and how to set up a Renormalization Group flow. Finally, I will discuss how Renormalization Group fixed points are related to the continuum limit in these discrete models, and will present explicit results on scaling exponents.
Enss Tilman
Title: Polarons in ultracold atomic gases
Abstract: The functional renormalization group has proved to be a powerful and reliable tool to study strongly correlated quantum fluids, as realized for instance with ultracold atoms. In this talk we will discuss the polaron problem of a mobile impurity interacting with a quantum degenerate gas. An impurity in a Fermi sea, the Fermi polaron, undergoes a transition to a molecular bound state if the attractive interaction becomes strong enough. We compute the spectral functions of the polaron and molecular states using an fRG approach with full self-energy feedback. By including the flow of the full frequency and momentum dependence of both the fermion self-energy and the interaction, we find that the spectra strongly deviate from a simple quasi-particle form. These results have recently been verified experimentally.
Gies Holger
Title: RG flow of the Higgs potential
Abstract: TBA
Herbut Igor
Title: Non-Fermi liquid vs. topological Mott insulator in electronic systems with parabolic band touching in three dimensions
Abstract: I will review the recent work on the phases and quantum phase transitions in the electronic systems that feature the parabolic band touching at the Fermi level, the celebrated and well-studied example of which is the bilayer graphene. In particular, it will be argued that three dimensional such systems are in principle unstable towards the spontaneous formation of the strong topological Mott insulator at weak long-range Coulomb interaction. The mechanism of the instability can be understood as the collision of non-Fermi liquid fixed point, discovered by Abrikosov in the `70s and revisited recently, with another, critical, fixed point, which approaches it in the coupling space as the system's dimensionality approaches certain ``critical dimension" from above. Some universal characteristics of this scenario, the width of the non-Fermi liquid crossover regime, and the observability of the topological Mott phase in common gaplesssemiconductors such as gray tin or mercury tellurude will be discussed.
Komargodski Zohar
Title: The symmetries and irreversibility of the renormalization group flow
Abstract: We will review recent progress on the symmetries of fixed points of the renormalization group flow as well as the irreversible nature of the flow.
Metzner Walter
Title: Spontaneous symmetry breaking in fermion systems with functional RG. II
Abstract: Spontaneous symmetry breaking is a ubiquitous phenomenon in many branches of physics. In solids, spontaneous symmetry breaking is often caused by interactions between electrons, that is, fermions. In our lecture we review how spontaneous symmetry breaking in interacting fermion systems can be treated by the functional renormalization group. There are two distinct ways of implementing spontaneous symmetry breaking in fermion systems. One approach is a purely fermionic flow with an order parameter leading to anomalous propagators and interaction vertices. Another possibility is to decouple the two-fermion interaction by a bosonic order parameter field, via a Hubbard-Stratonovich transformation, and to compute the coupled flow involving fermions and order parameter fields. We discuss both approaches, using U(1) symmetry breaking in fermionic superfluids as a prototypical example for the case of a broken continuous symmetry with an emergent Goldstone mode.
Morris Tim
Title: Tests of asymptotic safety beyond polynomial approximations
Abstract: TBA
Nishida Yusuke
Title: Few-body universality and (super) Efimov effect
Abstract: Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. In this talk, I will give a pedagogical introduction to the Efimov effect and then discuss our recent discovery of new few-body universality called super Efimov effect.
Nitti Francesco
Title: Holographic RG flows and quantum effective actions
Abstract:The AdS/ CFT correspondence offers a geometric realization of the quantum field theory renormalizaion group flows. I will describe the connection between QFT local RG transformations and radial diffeomorphisms, and show how beta-functions for space-time-dependent couplings can be computed from the bulk Einstein equations. Using a derivative expansion, I will show how one can write general, explicit expressions for the renormalized holographic generating functional, whose independence of the radial coordinate gives rise to holographic RG equations.
Percacci Roberto
Title: ERG and gravity: recent developments
Abstract: I will review some recent work on the application of the ERG to gravity focusing mainly on bi-metric and functional truncations.
Rancon Adam
Title: Fate of the amplitude mode in the vicinity of a quantum critical point
Abstract: The quantum O(N) model is ubiquitous in condensed matter and cold atoms and describes the behavior of a number of systems close to a quantum phase transition. In the ordered (broken-symmetry) phase far from the critical point, there are N-1 Goldstone modes and a gapped amplitude mode. In low imensions, the system is strongly coupled close to the critical point, and the existence of the amplitude mode is not guaranteed. We discuss the fate of the amplitude mode for N \geq 2 at zero and finite temperature using a non-perturbative renormalization group approach. For N=2, we find a well-defined resonance, in agreement with recent Monte-Carlo simulations. The resonance persists at finite temperature below the Kosterlitz-Thouless transition temperature. Furthermore, we show that the resonance is strongly suppressed for N \geq 3.
Reuther Johannes
Title: Cluster Functional Renormalization Group
Abstract: In the usual implementation of the functional renormalization group (FRG) method, the expansion point at which the diagrammatic resummation procedure is initiated corresponds to a free UV limit. In this work, we formulate a generalized version of the FRG where the UV limit consists of decoupled subsystems (clusters of sites). While the intra-cluster couplings are treated exactly, the inter-cluster couplings are addressed via RG. We particularly implement this method within the framework of the pseudofermion FRG for spin systems. As a benchmark study, we apply our cluster FRG scheme to the spin-1/2 bilayer Heisenberg model on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for this model, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.
Salmhofer Manfred
Title: Renormalization Group and Van Hove Singularities
Abstract: TBA
Schaefer Bernd-Jochen
Title: Phase structure, Thermodynamics and Fluctuations in QCD
Abstract: The possible emergence of a critical endpoint is one of the distinctive features of the finite temperature and density phase diagram of strongly-interacting matter. With QCD-inspired models the relevant high-density region in the phase diagram can be accessed. I review recent theoretical progress in our understanding of the QCD phase diagram, the role of fluctuations and applications in heavy-ion collisions. Specifically, results are discussed for the nature of the chiral and confinement-deconfinement phase transitions, their interrelation, and for thermodynamics as well as finite volume effects.
Scherer Michael
Title: FRG approach to graphene/multiorbital models
Abstract: Graphene consists of one single layer of carbon atoms organized on a honeycomb lattice and allows for a condensed-matter realization of the Dirac equation, where the electrons behave as massless Dirac fermions. The experimental observation of massless Dirac fermions in monolayer graphene has generated tremendous research activities in the last years and electrons in charge-neutral graphene embody a typical example of an interacting relativistic quantum system. Modifications of graphene by electron/hole doping or by adding additional layers allow to tune the density of states of the charge carriers and to enhance the role of interactions giving rise to instabilities and phase transitions towards symmetry broken phases. The phase diagram of graphene includes antiferromagnetic spin and charge density waves, unconventional superconducting phases and also more exotic topological states depending on the investigated parameter regime. In my talk I will briefly introduce the basics of graphene physics and then review recent findings on fixed-points, instabilities and the phase diagram for interacting electrons on graphene's honeycomb lattice and its modifications that have been obtained by means of (functional) renormalization group methods. Further, I will discuss some perspectives that I consider interesting for future research activities in this field.
Serreau Julien
Title: Nonperturbative infrared dynamics of interacting scalar fields in de Sitter space
Abstract: The understanding of quantum effects in curved spacetimes is a pressing issue in the context of modern cosmology. The quantum dynamics of light scalar fields in de Sitter space - the simplest cosmological spacetime which also describes a phase of accelerated expansion in the early Universe known as inflation - exhibits specific infrared divergences which have no analog in flat spacetime and which require resummation. I will discuss recent progress in generalizing known techniques, such as the large-N expansion or the nonperturbative renormalization group to de Sitter space, and present some results concerning the nonperturbative infrared dynamics of O(N) scalar fields. In particular, I will discuss the phenomenon of radiative symmetry restoration in de Sitter space.
Stergiou Andreas
Title: Aspects of RG flows in even spacetime dimensions
Abstract: Powerful constraints on RG flows in any even spacetime dimension can be found with a treatment based on the local RG. We will review recent results of this approach, focusing mainly on RG flows of four- and six-dimensional quantum field theories. We will elaborate on the a-theorem and the relation between scale and conformal invariance, and draw attention to pertinent new features encountered in dimensions higher than four.
Strack Philipp
Title: Hyperthermal matter beyond KPZ and superfluid matter beyond BCS
Abstract: We discuss two recent applications of the Wetterich equation to new
states of matter: (i) first, to extensions of the Burgers-Kardar-Parisi-Zhang to systems with 1/f-noise and (ii) second, to exotic pairing in imbalanced, charge-neutral Fermi gases. In (ii), we provide evidence for a quantum phase transition to superfluid states
with large Fermi surfaces (Sarma-Liu-Wilczek states) using the
effective potential flow equation discretized in field space. Such physics
is currently pursued in experimental quantum optics labs with ultracold atoms. In (i), motivated by recent connections of quantum liquids to KPZ scaling,
we provide a one-loop RG analysis of the KPZ equation with 1/f noise which
generalizes the KPZ universality to a natural example with broken Galilean invariance;
this leads to hyperthermal fixed points reminiscent to those found in turbulence.
Strodthoff Nils
Title: Spectral Functions from the Functional Renormalization Group
Abstract: In this talk I will give an overview about recent progress in the calculation of spectral functions within the framework of the Functional Renormalization group. As a concrete example I will mainly concentrate on the calculation of mesonic spectral functions within effective models for QCD but I will also illustrate the calculation of transport coefficients where single-particle spectral functions serve as input.
Weise Wolfram
Title: Nuclear Chiral Thermodynamics and the Functional Renormalization Group
Abstract: Non-perturbative mesonic (in particular: pionic) fluctuations in symmetric and asymmetric nuclear matter as well as in neutron matter are studied starting from a chiral nucleon-meson Lagrangian and using FRG methods. The resulting systematics of the nuclear phase diagram (the nuclear liquid-gas transition and its disappearance with increasing proton-to-neutron ratio) turn out to be remarkably close to results of three-loop in-medium chiral effective field theory calculations. The chiral order parameter in both symmetric nuclear matter and neutron matter is explored. It is generally found that dynamics beyond mean-field approximation shifts the tendency towards chiral symmetry restoration to very high baryon densities, much above three times the density of normal nuclear matter in equilibrium. Extrapolations to neutron star matter and corresponding constraints are also discussed.
Wschebor Nicolas
Title: On the relation of Non-Perturbative Renormalization Group and the conformal symmetry in arbitrary dimension
Abstract: In presence of an infrared regulator as used in Non-Perturbative Renormalization Group (NPRG) equations, the Ward identities for scale invariance are modified giving relations that are nothing but the equations that come from the fixed point condition of NPRG equations. We present here how Ward identities for special conformal transformations are modified in presence of such an infrared regulator. As an example of application, we suggest how those equations can be used in order to prove that scale invariance implies conformal invariance in any dimension for all scalar O(N) models. (work in collaboration with B. Delamotte and M. Tissier)
Zanusso Omar
Title: Functional renormalization group and statistical mechanics of membranes
Abstract: We will first review the distinct universality classes of membranes, determined by the membrane's local order, and the models developed to describe them. We will then discuss the recent applications of the non-perturbative renormalization group to these models aimed at improving the understanding of the membranes' phase-space beyond the epsilon-expansion. Finally, we will comment on the implications of these results on various physical systems.