Research focus: computational methods, condensed-matter and quantum many-body physics
The research interests of the group of Uli Schollwöck focus on the computational study of many-body systems that show strong interaction effects such that conventional many-body perturbation techniques mostly do not work. Such systems range from quantum spin chains, frustrated quantum magnets through low-dimensional superconductors and conjugate polymers to ultracold atom gases in optical lattices, which are particularly important for us: The merger between traditional condensed matter physics and quantum optics is a special focus of our work.
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. In low dimensional quantum systems, methods of choice are the density-matrix renormalization group (DMRG), which is a variational method within the ansatz class of matrix product states (MPS), and arguably the most powerful method for one-dimensional quantum systems, and tensor network states (TNS). 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 also interested in merging this method with the dynamical mean-field theory (DMFT) and in developing new algorithms at finite temperature and for higher dimensions.