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.
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, expansion experiments, 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. 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.
In the context of out-of-equilibrium physics, recent highlights of our research include the first dynamical quantum simulator, which resulted from a collaboration with the Bloch group, the development of expansion dynamics in the presence of optical lattices as a tool to study interactions and probe integrability vs. non-integrability in quantum systems, and the dynamics of (spin) impurities in magnets simulated by ultracold atoms.
We are also pushing applications of conventional DMRG to two-dimensional quantum systems: while this is an exponentially hard task in the thermodynamic limit, the very high numerical stability of the method allows us to obtain very precise results on such quantum systems nevertheless. A recent highlight was the identification of the topological nature of the spin liquid ground state of a key model in frustrated magnetism, the kagome Heisenberg model, where we determined the topological entanglement entropy.
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.