P4 (2013)

Time evolution using DMRG methods for spin and fermionic systems coupled to bosonic degrees of freedom.

Fabian Heidrich-Meisner, Eric Jeckelmann, Ulrich Schollwöck

The main goal of this project is the development of efficient and versatile computational meth- ods for studying the nonequilibrium dynamics of strongly correlated quantum systems with bosonic degrees of freedom. These methods will be based on one of the most powerful nu- merical approaches for low-dimensional quantum systems, the density-matrix renormalization group (DMRG) method in the matrix-product-state/tensor-network framework. This will be achieved by combining the efficient DMRG techniques for bosons developed in the 1990s with the DMRG algorithms for simulating the time evolution of quantum systems, which have been introduced in the last few years. The new algorithms will be adapted and tested for a broad va- riety of timely problems from condensed matter physics involving strongly correlated bosons out of equilibrium. They include nonequilibrium and dissipative transport in nanostructures, equilibrium and time-resolved spectroscopy of quasi-one-dimensional materials and nanosys- tems, photoinduced phase transitions in low-dimensional materials, and quantum quenches of ultra-cold gases in optical lattices.