# Talks

#### Jürgen Berges

**Non-thermal fixed points**

Strongly correlated systems far from equilibrium can exhibit scaling
solutions with a dynamically generated weak coupling. We show this by
investigating isolated systems described by relativistic quantum field
theories for initial conditions leading to nonequilibrium
instabilities, such as parametric resonance or spinodal decomposition.
The non-thermal fixed points prevent fast thermalization if
classical-statistical fluctuations dominate over quantum fluctuations.
We comment on the possible significance of these results for the
heating of the early universe after inflation and the question of fast
thermalization in heavy-ion collision experiments.

#### Claude Bervillier

**Analytical approximation schemes for solving exact renormalization group equations**

Abstract : We present and compare four new and efficient analytical approximation schemes to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. We consider, for the scalar field, the local potential approximations of the Wegner-Houghton equation in the dimension d=3 and of the Wilson-Polchinski equation for some values of $d\in \left[ 2,3\right] $. We also consider, for d=3, the coupled ODEs obtained by Morris at the second order of the derivative expansion. In both cases the fixed points and the eigenvalues attached to them are estimated. Comparisons of the results obtained are made with the shooting method.

#### Jens Braun

**Towards Bridging the Gap Between Quarks and Gluons and Baryonic Degrees of Freedom**

I give a review of some of the current challenging
problems of QCD. I discuss the chiral phase transition in QCD with
its underlying mechanisms in terms of quarks and gluons
and present results for the chiral phase boundary in
the plane of temperature and number of (massless) quark flavors
obtained from a functional renormalization group approach.
Moreover, the dependence of the phase transition temperature on the
quark chemical potential is discussed. The last part of the talk deals with
the deconfinement phase transition in Yang-Mills theory. The order-parameter
potential for SU(3) Yang-Mills theory, namely the Polyakov-loop
potential, obtained from a functional renormalization group study is shown.

#### Leonie Canet

**Strong-coupling regime of the Kardar-Parisi-Zhang equation**

The celebrated Kardar-Parisi-Zhang equation,
initially derived as a model to describe the kinetic roughening of a
growing interface, has given rise to intense theoretical investigations for
over two decades since it stands as a simple - yet unsolved - model for
scaling phenomena and non-equilibrium phase transitions.

The problem is that the scaling rough phase of the KPZ equation
corresponds to a strong-coupling
fixed point and has remained out of reach of perturbative methods so far.
We show that a non-perturbative renormalisation group approach
provides a controlled analytical tool to describe this fixed-point
and investigate the statistical properties of the rough interface profile.

#### Sebastian Diehl

**Towards precision in the BCS-BEC crossover in ultracold fermion systems**

The Functional Renormalization Group (FRG) is used for a study of the
crossover problem. A unified picture for the whole phase diagram is obtained. Various
effects beyond Mean field theory are included. The fluctuations of an
effective, dynamically generated boson field are found to be crucial:
Bosonic vacuum fluctuations contribute to the ratio of molecular to fermionic
scattering length, while thermal fluctuations are necessary to establish the
expected second order nature of the phase transition throughout the
crossover. The FRG approach further enables us to reconstruct the effects of particle
hole fluctuations, which impact e.g. on the critical temperature.

#### Nicholas Dupuis

**Non-perturbative renormalization group approach to superfluidity**

We use the non-perturbative renormalization group to solve the problem of infrared divergences occurring in the perturbation theory of interacting boson systems. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all dimensions $d>1$. For $d\leq 3$, the fixed point is characterized by an SO(d+1) space-time symmetry. In one-dimension and for not too strong interactions, we obtain a good picture of the Luttinger-liquid behavior of the superfluid phase. We comment about the relevance of these results for the understanding of the Mott-superfluid transition in the Bose-Hubbard model.

#### Stefan Floerchinger

**Functional renormalization for ultracold quantum gases**

Using the functional renormalization group, we study the effect of thermal and quantum fluctuations in ultracold nonrelativistic quantum gases. For a single component Bose gas, we determine the phase diagram and calculate a branch of thermodynamic observables in both three and two spatial dimensions. We also investigate systems with Fermions using the methods of partial bosonization. For example, we investigate the phase diagram and especially the effect of particle-hole fluctuations in the BEC-BCS crossover of two Fermion species.

#### Thomas Gasenzer

**Functional Renormalisation Group approach to Far-From-Equilibrium Quantum Field Dynamics**

Dynamic equations for quantum fields far from equilibrium are derived
by use of functional renormalisation group techniques. The obtained
equations are non-perturbative and lead substantially beyond
mean-field and quantum Boltzmann type approximations. The approach is
based on a regularised version of the generating functional for
correlation functions where times greater than a chosen cutoff time
are suppressed. As a central result, a time evolution equation for
the non-equilibrium effective action is derived, and the
time-evolution of the Green functions is computed within a vertex
expansion. It is shown that this agrees with the dynamics derived from
the 1/N-expansion of the two-particle irreducible effective
action.

#### Carsten Honerkamp

**Functional renormalization group for interacting fermions in 2D - recent applications and improvements**

The functional renormalization group for fermions has become a powerful
tool for the analysis of many-fermion systems, in particular for cases
with competing interactions. Here review some recent applications of the
method in the 'standard approximation' and describe efforts underway to
improve the method beyond this level.

#### Christoph Husemann

**Competing Orders in the Hubbard Model at van Hove Filling**

One-loop renormalization group techniques have been successful in
determining weak coupling instabilities of the two-dimensional Hubbard
model using an N-patch discretization of momentum space. We propose a more
efficient parametrization of the four-point vertex function, which is
based on decomposing the effective two-fermion interaction in interacting
fermion bilinears.

#### Yuji Igarashi

**Quantum Master Equation for Yang-Mills Theory in ERG**

We discuss a general functional method for construction of
the Quantum Master Equation in the Batalin-Vilkovisky
antifield formalism for Yang-Mills theory in the exact renormalization group.

#### Etsuko Itou

**The BV Master Equation for the Gauge Wilson Action**

The Wilson effective action for general Yang-Mills
gauge theory is shown to satisfy the usual form
of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff
apparently breaks the gauge invariance. In the
case of Abelian gauge theory, in particular, it actually deduces the
Ward-Takahashi identity for Wilson action recently
derived by Sonoda.

#### Pawel Jakubczyk

**Renormalization group for phases with broken discrete symmetry near quantum critical points**

We extend the Hertz-Millis theory of quantum phase transitions in
itinerant electron systems to phases with broken discrete symmetry.
Using a set of coupled flow equations derived within the functional
renormalization group framework, we compute the second order phase
transition line T_c(delta), with delta a non-thermal control parameter,
near a quantum critical point. We analyze the interplay and relative
importance of quantum and classical fluctuations at different energy
scales, and we compare the Ginzburg temperature T_G to the transition
temperature T_c, the latter being associated with a non-Gaussian
fixed-point.

#### Christoph Karrasch

**A finite-frequency functional RG approach to the single impurity Anderson model**

We use the Matsubara functional renormalization group to calculate
finite-energy properties of the single impurity Anderson model. To this
end, we account for the frequency-dependence of the two-particle vertex.
The FRG approximation is shown to work well for arbitrary parameters
(particularly finite temperatures) provided that the electron-electron
interaction $U$ is not too large. In contrast, it turns out that aspects of
(large $U$) Kondo physics which are described well by a simpler
frequency-independent truncation scheme are no longer captured by the
`higher-order' frequency-dependent approximation. We suggest to parametrize
the two-particle vertex not by three independent energy variables but by
introducing three functions each of a single frequency, considerably
reducing the numerical effort to integrate the FRG flow equations.

#### Andrey Katanin

**The two-loop functional renormalization group approach to the one- and two-dimensional Hubbard model**

I consider the application of the two-loop functional renormalization-group
(fRG) approach to study the low-dimensional Hubbard models. This approach
accounts for both, the universal and non-universal contributions to the RG
flow. While the universal contributions were studied previously within the
field-theoretical RG for the one-dimensional Hubbard model with linearized
electronic dispersion and the two-dimensional Hubbard model with flat Fermi
surface, the non-universal contributions to the flow of the vertices and
susceptibilities appear to be important at large momenta scales. The
two-loop fRG approach is also applied to the two-dimensional Hubbard model
with a curved Fermi surface and the van Hove singularities near the Fermi
level. I show that the vertices and susceptibilities in the end of the flow
of the
two-loop approch are suppressed in comparison with both the one-loop
approach, the quasiparticle weight remains finite in two dimensions at not
too low temperatures above the paramagnetic ground state.

#### Stefan Kehrein

**Flow equations and nonequilibrium quantum many-body physics**

Quantum many-body systems in nonequilibrium situations, either due to
initial preparation in a non-thermal state or in driven systems, have
recently
become of considerable interest because of experimental realizations in
ultracold atomic gases and in electronic nanostructures. Since the
flow equation
method retains the full Hilbert space, it is very well suited for
studying such
highly excited quantum systems. In this talk I will present two
applications of
this approach to models of paradigmatic importance in condensed matter
physics: The Kondo model with external voltage bias and an interaction
quench in a Fermi liquid.

#### Bertram Klein

**Critical scaling behavior in the O(N) model in infinite and finite volume**

We use the functional RG to obtain universal scaling functions for O
(N) models in three dimensions in the presence of an explicitly
symmetry-breaking field. Our results are in good agreement with those
of O(N) spin model simulations on the lattice. Applying the same RG
technique to a finite-volume system, we are also able to determine
the finite-size scaling functions for this universality class. These
scaling functions are relevant for the analysis of the chiral phase
transition behavior in lattice simulations of Quantum Chromodynamics,
where both symmetry-breaking and finite-volume cutoff effects are
important.

#### Peter Kopietz

**Functional renormalization group approach to interacting fermions with partial bosonization: from weak to strong coupling**

We show that for certain model systems
the functional renormalization group approach
to interacting Fermi systems with partial bosonization via
suitable Hubbard Stratonovich fields developed by
Schtz, Bartosch and Kopietz [Phys. Rev. B 72, 035107 (2005)]
can be used to explore the strong coupling regime.
In particular, use this method to show that strong interactions
can give rise to a confinement transition in quasi one-dimensional
metals, where
in the strong coupling regime the curvature of the Fermi surface
is completely smoothed out [Ledowski and Kopietz, Phys. Rev. B 76,
121403(R), 2007].
We also present preliminary results
for the Anderson impurity model, where
a non-perturbative treatment of the spin-flip scattering is crucial
to remove the unphysical ferromagnetic instability encountered at the
mean-field level
and to describe the strong coupling Fermi liquid fixed point.

#### Hans Christian Krahl

**A Functional Renormalization Group approach to the Hubbard model**

Within the two-dimensional repulsive t-t'-Hubbard model, an attractive coupling in the d-wave pairing channel is induced by fluctuations of antiferromagnetic spin waves. We investigate this coupling using functional renormalization group equations. The momentum dependent d-wave coupling can be bosonized by the use of scale dependent field transformations. We propose an effective coarse grained model for the Hubbard model which is based on the exchange of antiferromagnetic and $d$-wave collective bosons.

#### Oliver Lauscher

**Projected flow equations and competing ordering tendencies in the 2D Hubbard model**

The competition of different ordering tendencies in the two-dimensional
$t$-$t'$-Hubbard model is analyzed on the basis of the fermionic
weak-coupling RG approach. We study the RG flow of the 4-point vertex in a
truncated interaction space spanned by the on-site term, two spin-spin
interaction terms, a d-wave SC term and a $d$-density wave term. By
constructing appropriate projectors and applying them onto the RG equation
for the 4-point vertex we derive the set of RG equations for the couplings
parametrizing the truncated interaction subspace. These equations lend
themselves to profound numerical studies. First results at zero
temperature are already available.

#### Daniel Litim

**Optimisation and the functional RG**

I review optimisation ideas for flow equations from a conceptual and a
practical point of view, and illustrate their relevance and applicability
through a number of examples.

#### Volker Meden

**Functional RG for transport through quantum dots**

I discuss the application of approximation schemes
which are based on the functional RG to study correlation effects in quantum
dots. As a first example I describe transport through multi-level dots.
Depending on the ratio between the typical single-paricle level spacing and
the typical level broadening the transmission amplitude and the transmission
phase show characteristic behavior. Secondly, I discuss the Josephson
current through a single-level dot coupled to superconducting leads. The physics is
goverend by a phase transition. Our approach allows for a detailed study of
the dependence on all parameters. I emphasize that both studies are relevant
in connection with recent and ongoing experiments. I give a brief outlook on
the possible extensions of the approximate method (see also the talks by C.
Karrasch and M. Pletyukhov).

#### Yannick Meurice

**Linear and Nonlinear Aspects of Finite Size Scaling**

Starting with the general theory of finite size
scaling, we compare the size of linear and nonlinear effects for the
estimation of Binder cumulants of various spin and gauge models.
We propose a new strategy to resolve the nonuniversal corrections using
improved actions in the limit of small lattice size.
We discuss the applicability of the method for the hierarchical model,
the 3D Ising model and 4D lattice gauge theory.

#### Dominique Mouhanna

**Nonperturbative renormalization group approach to frustrated magnets**

Frustrated magnets, i.e. magnetic systems with competing interactions,
display a puzzling phenomenology: they exhibit scaling behaviors without
universality.
Moreover the perturbative approaches to these systems 1) fail to describe
this specific critical behavior and 2) are in conflict. I show, in this talk, how a
nonperturbative renormalization group approach allows both to correctly described
the phenomenology of frustrated magnets and to get a coherent picture of the
different theoretical approaches used. As a surprising consequence of our approach,
it appears that a high-order - 6 loops - perturbative approach performed at fixed dimension leads to
spurious predictions for these systems.

#### Sandor Nagy

**Renormalization of the Sine-Gordon model**

The critical behaviour of the correlation length of two-dimensional
sine-Gordon model has been determined by the functional renormalization
group method performed in the internal space including wave-function
renormalization. The results provides the treatment of the
Kosterlitz-Thouless-Berezinski type phase transition directly in the
sine-Gordon model. It is also obtained that the role of the higher Fourier
modes is not negligible.

#### Jan Martin Pawlowski

**Strong correlations in gauge theories**

In recent years much progress has been made in the understanding of
the strongly correlated sector of QCD. Most notably we understand, to
a large extend, the confinement mechanism and the related confinement
scenario. Moreover we have access to quantitative computations of
physical observables such as the order parameters of the
confinement-deconfinement and chiral phase transition.

I review the present status of the functional RG approach to gauge
theories. Results on the confinement mechanism and the
confinement-deconfinement phase transition in QCD are summarised,
including a comparison to other approaches, such as lattice gauge
theories and Dyson-Schwinger equations. I close with a discussion of
prospects for a first principle study of the QCD phase diagram and the
remaining problems.

#### Roberto Percacci

**Wilsonian investigations into the UV properties of gravity**

I will review recent progress suggesting that gravity may
be renormalizable at a nontrivial fixed point, along the
lines of the "asymptotic safety" programme.
Whenever possible, connection with other approaches will be made.

#### Massimo Pietroni

**Dealing with non-linearities in Cosmology**

To extend the program of precision cosmology to the study of the Large Scale Structure of the Universe it is mandatory to deal with non-linear fluctuations of the density and velocity fields. We will present two, RG-inspired, approaches to resum perturbative contributions to all orders. Results for the matter power spectrum will be presented and compared to the state of the art of other approaches.

#### Frank Reininghaus

**Dephasing rates within nonequilibrium RG: A generic approach**

We consider a generic model for a local quantum system coupled to
reservoirs and present a general solution to the problem how relaxation
and dephasing rates can be implemented within nonequilibrium
renormalization group. Generalizing previous RG-methods to a
specific frequency representation and using a cutoff on the imaginary
frequency axis, we show that decay rates always cut off the RG
flow and find the physical meaning of these rates. We illustrate the
method for the nonequilibrium Kondo model in a finite magnetic field h
and present results for the magnetic susceptibility and the differential
conductance in the weak coupling regime, where the RG equations can be
solved analytically in a controlled way by expanding in the exchange
coupling J. We find that the conductance is enhanced at specific
values V=h/n (n=1,2, ...) of the voltage.

#### Urko Reinosa

**Renormalization and gauge symmetry of 2PI effective actions**

In recent years, functional methods based on two-particle-irreducible
effective actions have known a renewed interest in problems involving
quantum fields in- and out-of-equilibrium. Still, the application of
these techniques to quantum gauge fields suffers from difficulties related
to symmetry and renormalization. I will discuss these problems and
report on recent progress in tackling them.

#### Martin Reuter

**Background independence and asymptotic safety in Quantum Einstein Gravity**

We review some basic concepts of the asymptotic
safety approach to quantum gravity and its
implementation in terms of the effective average
action, with an emphasis on its background
independence. As any consistent theory of quantum
gravity is supposed to explain rather than
postulate spacetime, the requirement of background
independence is the crucial difference between
matter quantum field theories and gravity. By
means of a simple example (conformally reduced
gravity) we demonstrate that the background
independent quantization of Einstein gravity leads
to a RG flow which differs significantly from the
one obtained on a rigid background. In particular
background independence seems to be important for
asymptotic safety.

#### Oliver Rosten

**Invariants of the ERG**

I will construct a functional, the `dual action', which, formally at any rate, is an invariant (ie has vanishing flow) of
Polchinski-like ERG equations. The relationship between the dual action
and the Wilsonian effective action can be easily inverted. However, if the
integrated ERG kernel is massless, this construction generically suffers
from infra-red problems. I will discuss what this means, and under what
circumstances the dual action might be a useful.

#### Bernd-Jochen Schaefer

**Exploring the QCD phase diagram with Functional RG**

The phase structure of various effective quark-meson models for two and
three quark flavors are presented. The impact of the Polyakov loop dynamics
on the phase diagrams is also briefly addressed. All models exhibit a
critical endpoint where fluctuations become important. The influence of
fluctuations around criticality is demonstrated by an comparison of the
mean-field approximation with a renormalization group analysis.

#### Krishnendu Sengupta

**Superfluid-Insuator transitions of bosons on a Kagome lattice at non-integer fillings**

In this talk, I shall describe the quantum phase
transition of bosons in a Kagome lattice at non-integer fillings and
describe the possible Mott states of the systems. Our results are based
on
a dual description of the bosons in terms of vortices and are supplemented
by Quantum Monte Carlo studies. These results are also relevant for XXZ
models on Kagome lattice. We shall describe the critical theory for this
transition and point out the possible role of NPRG in extracting relevant
information from this critical theory.

#### Hidenori Sonoda

**Simple recipe for realization of symmetry using ERG**

The talk will consist of three parts. In part 1 I briefly describe how
to modify the ERG differential equation to facilitate perturbative
calculations of the critical exponents of the Wilson-Fisher fixed
point. In part 2 I explain how to construct perturbatively
renormalizable theories using ERG. I emphasize that the correlation
functions calculated with a cutoff action is independent of the cutoff.
In part 3 I describe a general framework to incorporate symmetry (global
and local) using ERG.

#### Philipp Strack

**Fermion-boson RG for the ground-state of fermionic superfluids**

We present a comprehensive analysis of quantum
fluctuation effects in the superfluid ground state of an attractively
interacting Fermi system, employing the attractive Hubbard model as a
prototype. The superfluid order parameter, and fluctuations thereof,
are implemented by a bosonic Hubbard-Stratonovich field, which splits
into two components corresponding to longitudinal and transverse
(Goldstone) fluctuations. The flow equations derived capture the
influence of fluctuations on non-universal quantities such as the
fermionic gap, as well as the universal infrared asymptotics present in
every fermionic superfluid. We solve the flow equations numerically in
two dimensions and compute the asymptotic behavior analytically in two
and three dimensions. In the infrared regime, transverse order
parameter fluctuations associated with the Goldstone mode lead to a
strong renormalization of longitudinal fluctuations in agreement with
the exact behavior of an interacting Bose gas.

#### Haruhiko Terao

**Conformal extension of the Higgs sector and the little hierarchy problem**

After a brief review of the little hierarchy
problem of the SM, we consider a new possibility in the Higgs sector
above the TeV scale. There it is assumed that the Higgs scalar acquires
a large anomalous dimension induced by a conformally invariant Yukawa
coupling. We examine the infrared fixed point of gauge-Yukawa theories
by means of the ERG equations in a rough aaproximation scheme and show
that sufficiently large anomalous dimensions can be realized there.
We also present a concrete phenomenological model, which may pass the
EW precision tests.

#### Nikolaos Tetradis

**Effective field theory with a variable ultraviolet cutoff**

The properties of strongly gravitating systems
suggest that field theory overcounts the states of a system. Reducing the
number of degrees of freedom, without abandoning the notion of effective
field theory, may be achieved through a connection between the ultraviolet
and infrared cutoffs. I present an implementation of this idea within the
Wilsonian approach to the renormalization group. An exact flow equation
describes the evolution of the effective action. I discuss the
implications for the existence of infrared fixed points and the running of
couplings.

#### Shan-Wen Tsai

**Effects of retardation in the functional renormalization group approach to interacting fermions**

When fermion-fermion interactions are frequency dependent,
there are important retardation effects in the functional RG flows of
vertices and correlation functions. I will discuss these effects and
show that they may change the phase diagram and the critical energy
scales. I will also present results for the case of electron-phonon
systems, and for mixtures of fermionic cold atoms in the presence of a
Bose-Einstein condensate.

#### Michael Weyrauch

**Beyond the static approximation in the fermionic renormalization group**

I briefly review a variant of the fermionic fRG
using an additive cutoff instead
of the standard multiplicative cutoff for the free propagator. I apply
this approach to Hubbard models of 1D rings
and quantum dot systems. Comparisons are made with DMRG calculations.

#### Peter Wölfle

**Transport of interacting electrons through a potential barrier: nonperturbative RG approach**

We calculate the linear response conductance of electrons in a Luttinger
liquid with arbitrary interaction g2, and subject to a potential barrier of
arbitrary strength, as a function of temperature. We first map the
Hamiltonian in the basis of scattering states into an effective low
energy Hamiltonian in current algebra form. Analyzing the perturbation
theory in the fermionic representation the diagrams contributing to the
renormalization group (RG) Beta-function are identified. A universal part of
the Beta-function is given by a ladder series and summed to all orders
in g2. First non-universal corrections beyond the ladder series are
discussed. The RG-equation for the temperature dependent conductance is
solved analytically. Our result agrees with know limiting cases.
[D.N. Aristov, P. Wölfle, Europhys. Lett. 82, 27001 (2008)]

#### Nicolas Wschebor

**Precise NPRG calculation of critical exponents of the O(N) model**

A manageable approximation, formulated within
the NPRG, that goes beyond derivative expansion and field truncations
schemes, will be presented. It will be shown that it makes possible to
calculate in a standard personal computer the critical exponents for
the O(N) with at least the same accuracy that best field theoretical
methods.

# Posters

#### Michael Scherer

**Particle-hole fluctuations in the BEC-BCS crossover**

The effect of particle-hole fluctuations for the BEC-BCS crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length a. On the BCS side for small negative a we recover the Gorkov approximation, while on the BEC side of small positive a the particle-hole fluctuations play no important role. In the unitarity limit of infinite scattering length our result agrees with numerical simulations. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound state exchange.

#### Richard Schmidt

**Trion formation in ultracold fermion gases**

Using the functional renormalization group, we investigate the formation of bound states in a gas of three different nonrelativistic Fermion species. We employ a scale dependent bosonization and fermionization technique to investigate a model with global U(3) symmetry. Close to a Feshbach resonance, the fermions indeed form a fermionic bound state or trion.