The research interests of the Chair for Theoretical Nanophysics focus on many-body systems that are sufficiently small (typically, but not exclusively on the nanoscale) for quantum effects to play a dominant role or that show strong interaction effects. Such systems range from quantum spin chains, frustrated quantum magnets through low-dimensional superconductors and conjugate polymers to ultracold atom gases in optical lattices. The merger between traditional condensed matter physics and quantum optics is a special focus of our work.
While we have focused previously on the equilibrium and linear response regime, more advanced techniques now allow us to go very far from equilibrium, where physics is very poorly understood: we are looking at quantum quenches, transport properties and relaxation physics.
The dominant role of quantum and interaction effects usually implies that no simple analytical approximations are available. More advanced techniques, such as bosonization in one dimension or field theoretical approaches in arbitrary dimensions, have to be used. In the absence of a large number of exact solutions the ultimate test is in numerical approaches, which are a central part of our efforts. Here our interest is in both applying and developing these methods with a special emphasis on the guidance provided by insights from quantum information theory.
Starting from the density-matrix renormalization group (DMRG), we are currently interested in merging this method with the dynamical mean-field theory (DMFT) and in developing new algorithms at finite temperature and for higher dimensions based on the natural generalizations of DMRG provided by so-called tensor network states.