Our group studies the physical properties of quantum systems consisting
of a macroscopically large number of strongly interacting fermions.
These systems can show collective behavior that cannot be understood on
an independent-particle level.
The field covers collective magnetism, correlation-driven metal-insulator
transitions, high-temperature superconductivity and unconventional states
of matter in general.
We are interested in classical and quantum phase transitions in low-dimensional
lattice systems and nanostructures, in elementary excitation spectra and also
in non-equilibrium phenomena.
The employed methods range from field-theoretical techniques and exact
diagonalization over (dynamical) mean-field theory and cluster techniques
to (quantum) Monte-Carlo methods and density-matrix renormalization group.
An important focus is on new methodical developments.

Collective Magnetism

goals

investigation of conditions and characteristica of collective magnetic
order of itinerant valence electrons in metals
for inhomogeneous systems and systems with reduced translational symmetry
(surfaces, thin films, multi-layer systems, nanostructures)

development and application of dynamical (cluster) mean-field approaches
to study magnetic phase diagrams and single-electron excitation spectra

development and application of the variational matrix-product-state approach
to study magnetic correlations in one-dimensional nanochains

study of the role of electron correlations on exchange couplings and of
magnetic anisotropies in reorientation transitions

Self-Energy Functionals

goals

construction of new, non-perturbative and thermodynamically consistent
approaches to strongly correlated electron systems based on a novel
idea to evaluate classical (Luttinger-Ward) functionals of the self-energy

numerical implementation of different approximations within the self-energy-functional
appraoch (SFA)
to study its general features
(variational character, convergence, bath-sites concept, cluster approximations,
etc)

application of local and cluster approximations to standard lattice fermion models
(Hubbard, three-band Hubbard, periodic Anderson model, etc)

generalization of the theory: Bose systems, two-particle correlation functions,
off-site interactions, SFA-GW, SFA-QMC

Low-Temperature Phases of Underdoped Cuprates

goals

study of the global phase diagram of the high-temperature superconducting compounds and
the competition between the different phases in a tightly coordinated effort between sample
preparation, experiment and theoretical modeling

development and application of (partly) new theoretical techniques, namely
quantum Monte-Carlo (QMC), variational cluster techniques based on the
self-energy-functional approach (SFA), combined SFA-QMC scheme,
new contractor renormalization-group concepts (CORE)

clarify what is of "general relevance" and what is more "material specific"
in the high-Tc compounds

answer questions that are central for an understanding of the high-Tc phonomenon
(asymmetry of the phase diagram,
coupling of charge carriers to bosonic excitations,
role of electron-phonon interaction in the pairing mechanism,
nature of the pseudo-gap ``phase'', etc)

connect the microscopic interactions at
"high energy" (from eV to order J) with the observed phases competing with
each other at low temperatures (of the order of the superconducting gap)

Mott-Hubbard Systems

goals

development of a simplified theoretical approach to the Mott-Hubbard
metal-insulator transition
in Hubbard-type systems: "linearized dynamical mean-field theory"

computation of the critical interaction and the critical chemical potential
for different lattices and a as functions of band degeneracy and band
filling in multi-orbital models

analysis of the critical behavior in the vicinity of the Mott transition

further development of the theory in the non-critical regime: "two-site DMFT"

extension to multi-orbital systems

Theory of Electron Spectroscopies

goals

realistic description of angle-resolved photoemission spectroscopy
(and related electron spectroscopies)

inclusion of correlation effects

inclusion of final-state effects, selection rules, transition matrix elements, optical potential, etc.

electron spectroscopy beyond the linear-response regime, beyond the sudden approximation, etc.

Inhomogeneous Systems of Correlated Electrons

goals

formulation, development and application of the dynamical mean-field theory
(DMFT) as well as different standard many-body techniques for systems with
reduced translational symmetry

investigation of generic surface- and thin-film effects in systems of strongly
correlated electrons

phase diagram and excitation spectra of inhomogeneous low-dimensional systems