The functional renormalisation group (FRG) provides a way of studying
field theoretical and statistical-mechanical models systematically
as a function of a scale (e.g. a length scale or energy scale).
The scale parameter provides an infrared cutoff. The FRG equation
is a functional partial differential equation describing the change
of the generating functional under variation of the scale parameter.
As such, it is an equation that contains the full information about
the correlation functions. It therefore allows for exact studies
wherever possible and for a systematic improvement of approximations
in general.
The method has been applied to theories
on all energy scales, ranging from ultracold gases to
quantum gravity, both in equilibrium and for time-dependent phenomena.
In many cases, it has provided a detailed understanding
of phase diagrams and physical observables, and thus has made quantitative
the general RG idea how effective theories emerge from given
fundamental laws.
Important contributions to renormalisation group theory have been made
by people in Heidelberg,
and our institute is one of the major centers worldwide in this area.
- Theoretical aspects of the functional renormalisation group
- Mathematical renormalisation group methods
- Phase diagram and dynamics of ultracold atom gases
- Phase diagram and dynamics of QCD
- Quantum phase transitions
- Many-Fermion systems, Fermi liquid theory and its breakdown
- Non-equilibrium evolution of quantum systems
- Unconventional superconductivity and magnetism in models of correlated
electrons
- Gravity, cosmology and UV completions of the Standard Model
J.M. Pawlowski, M. Salmhofer, C. Wetterich
The functional renormalisation group is a method well-suited to study systems
recent publications
J.M. Pawlowski, M. Salmhofer, C. Wetterich
In preparation
recent publications
J.M. Pawlowski, M. Salmhofer, C. Wetterich
The physics of ultracold quantum gases is a novel area of research which evolves rapidly both experimentally and theoretically. One of the most interesting topics, studied extensively during recent years, is a proper understanding of the phase diagram of two-component fermions interacting via a simple contact two-body potential. At low temperature the system is superfluid and undergoes a smooth crossover from the BCS superfluid of atoms in the regime of weak interactions to the BEC of molecular dimers in the regime of strong interactions. From the theoretical perspective especially challenging is the unitarity regime, where no perturbative treatment is available. We are undertakening an extensive theoretical study of this many-body problem using the FRG method. As an interesting by-product, a number of results relevant for the universal few-body quantum physics (e.g. the Efimov effect) emerged.
recent publications
J.M. Pawlowski
QCD at finite temperature and finite density is is a very active area
of research, and is relevant for our understanding of current and
future experiments at LHC, RHIC and GSI. It is a strongly-correlated
system and its understanding requires non-perturbative methods such as
the FRG. In particular, at finite density FRG methods do not suffer
from a sign problem that hampers progress on the lattice.
Currently we study full dynamical QCD at density and temperature, and
map out the phase diagram of QCD with the help of order parameters for
confinement and chrial symmetry breaking. These studies are accompanied
by QCD-model studies with FRG methods as well as lattice computations.
Applications range from dynamical aspects of heavy ion collisions,
bound state formation to astrophysical implications of the QCD phase
diagram.
recent publications
C. Wetterich
A phase transition which happens at zero temperature and is governed by quantum effects is called a quantum phase transition. In general, this phase transition happens due to competition of two noncommuting operators in a Hamiltonian, each of which prefer a ground state with different symmetry properties. Quantum phase transitions are ubiquitous in various theoretical problems studied in condensed matter and statistical physics. Moreover, a number of modern experiments are done in the quantum degenerate regime and can probe quantum phase transitions directly. In our group we employ the method of the FRG to theoretically investigate quantum phase transitions in different many-body systems. In particular, we predicted novel quantum phase transitions in a three-component fermionic system with SU(3) symmetry. In addition, we currently investigate a quantum mixture of nonrelativistic bosons and fermions which also undergoes an interesting quantum phase transition.
recent publications
M. Salmhofer
In preparation
recent publications
T. Gasenzer, J.M. Pawlowski, M. Salmhofer, C. Wetterich
The dynamics of many-body quantum systems far from thermal equilibrium
is studied using a flow-equation approach on the basis of functional
renormalisation-group techniques. For real-time evolution one possible,
unconventional choice of the cutoff function is in the time-domain, in
accordance with causality. This allows to derive a set of Volterra-like
dynamic equations which can be solved in an iterative way. Presently
studied topics include beyond-standard nonperturbative approximation
techniques, with applications in the physics of strongly correlated
electron as well as ultracold atomic quantum gases.
recent publications
M. Salmhofer
In preparation
recent publications
J.M. Pawlowski, C. Wetterich
The asymptotic safety scenario of gravity is based upon a non-trivial
ultraviolet fixed point of gravity which circumvents the problem of
perturbative renormalisability. This is an interesting approach to
quantum gravity, and the FRG is a very natural method to access the
stability as well as the phenomenological consequences.
Currently we study the stability problem of gravity coupled to matter
and non-Abelian gauge fields, as well as the construction of fully
background and diffeomorphism invariant flows. We also work on the
phenomenological consequences of UV-safe gravity in large extra
dimensions for LHC predictions.
recent publications