
Project Area A: ManyBody Phenomena


A1 
Effective theories of correlated fermions 
J. von Delft, ASC München, K. Efetov, TP Bochum, P. Müller, M München 

In this project we study various effective theories for correlated fermion systems. In particular, we will (1) investigate bosonization in arbitrary dimensions as a tool for both analytics and Monte Carlo numerics; (2) develop effective field theories for disordered Luttinger liquids; (3) study transport properties of Josephson junctions and other granular materials; (4) study the behavior of the transmission phase through a quantum dot during the crossover from closed to open dots; (5) conduct a mathematical study of Andersonâ€™s orthogonality catastrophe in clean and disordered fermion systems; and (6) extend the JordanWigner transformation from linear structures to star geometries, allowing for an exact mapping of quantum spin chains in a star geometry to quantum impurity models. 




A3 
Nonlinear dynamics of strongly interacting quantum fields 
A. Altland, TP Köln, K. Hornberger, TP DuisburgEssen, S. Kehrein, ASC München, M. Kunze, M Köln, A. Rosch, TP Köln, R. Schützhold, TP DuisburgEssen 

The understanding of strongly interacting quantum manybody systems is one of the main challenges of contemporary physics. Even in those cases where the ground state of such a system is known, we are just beginning to understand their nonlinear dynamics. In this project, we study the impact of particle interactions by means of archetypical processes: a) the backreaction of quantum (or thermal) fluctuations onto the classical mean field and b) the decoherence, equilibration and thermalization dynamics of the system after a departure from the ground (or thermal equilibrium) state. Furthermore, we study the interplay of thermalization and dynamics by investigating the expansion of fermionic atoms in optical lattices where c) the breakdown of hydrodynamics is described by regularized singular diffusion equations. 




A4 
Nonequilibrium phenomena 
R. Egger, TP Düsseldorf, S. Kehrein, ASC München, R. Schützhold, TP DuisburgEssen 

This project is devoted to the theory of nonequilibrium phenomena in interacting mesoscopic quantum systems, in particular to conceptual foundations of timedependent transport and quantum phase transitions. Several interrelated subprojects aim at achieving progress in this important area. This includes the formulation and application of general fluctuation relations, the development of theoretical approaches for driven open quantum systems and timedependent quantum phase transitions, as well as questions of more applied relevance, such as currentinduced mechanical forces, or nonequilibrium phenomena in disordered Luttinger liquids. 




A5 
Mesocopic transport of Dirac fermions 
E. Efetov, TP Bochum, R. Egger, TP Düsseldorf, I. Eremin, TP Bochum 

Project A5 aims at a detailed understanding of Dirac fermions in mesoscopic systems. Physical realizations include graphene monolayers and the surface state of a strong topological insulator. The project is mainly concerned with interaction effects and with physicsmotivated research on experimentally relevant questions concerning mesoscopic quantum transport of Dirac fermions. 




A7 
Fluctuations and large deviations in nonequilibrium stochastic dynamics 
A. Altland, TP Köln, E. Frey, ASC München, J. Krug, TP Köln, C. Külske, M Bochum, A. Winter, M DuisburgEssen 

The project explores fluctuationdominated behavior in interacting manybody systems originating from a variety of physical and biological contexts. A common methodological basis is provided by the use of large deviations principles in path space, which links the project to dynamical systems theory and semiclassical quantum mechanics. Specific problems to be addressed concern the structure of noneequilibrium measures in spin systems, fluctuation theorems for mesoscopic quantum systems, and effects of demographic and spatial fluctuations in models of biological population dynamics. 




A8 
Nonabelian symmetries in tensor networks 
J. von Delft, TP München, P. Littelmann, M Köln, U. Schollwöck, TP München 

In the numerical simulation of quantummany body systems, the exploitation of symmetries is absolutely essential for the feasibility of certain calculations, in that they can provide orders of magnitude in performance gain. Given nonabelian symmetries, for example, for numerical procedures such as the diagonalization of Hamiltonians, the WignerEckart theorem can be utilized to significantly reduce the number of relevant matrix elements. In particular, this allows one to focus on symmetry multiplets only, instead of separately keeping track of all states within each multiplet. Though the added symmetry structure makes numerical codes significantly more complex,finally their performance can be dramatically improved. The project thus focuses on the efficient and transparent implementation of quantum symmetry spaces. These are to be applied to tensor network algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG) for 1dimensional quantum chain models, as well as the multiscale entanglement ansatz (MERA) and the projected entangledpair states (PEPS) Ansatz for twodimensional quantum lattice models. Moreover, the efficiency of algorithms for calculating the ClebschGordan coefficients for nonabelian groups such as SU(N) will be increased, by exploiting the Weyl symmetry of their weight diagrams. 




A9 
The spectrum of interacting fermions in graphene quantum dots 
R. Egger, TP Düsseldorf, H. Siedentop, M München, E. Stockmeyer, M München


The physical object of research in project A9 is defined by twodimensional graphene monolayers, where fermions (dressed electrons) can be delocalized or confined by a locally perturbed homogeneous magnetic field defining a quantum dot. We aim at the detailed understanding of spectra of Weyl operators (massless Dirac operators) describing interacting fermions in graphene.The fermions interact directly through Coulomb forces and, possibly, indirectly via phonon fields. The prime mathematical objects to be studied will be selfadjoint operators describing these systems. More precisely, these will be suitable Nparticle Hamiltonians, and those Hamiltonians coupled to phonon fields. 



