Matrix-product-state-based quantum impurity solvers

Ulrich Schollwöck


The purpose of this project is to advance the status of quantum impurity solvers that are based on matrix product states, i.e. to calculate the local spectral function for a cluster of correlated sites embedded in an external bath consisting possibly of multiple external bands. In the first phase of FOR 1807, the performance of such impurity solvers (either based on Chebyshev polynomials or the Fourier transformation of time-evolutions, combined with a linear prediction technique) could be pushed so far that for the first time equilibrium  dynamical mean-field theory (DMFT) can be studied using matrix product states for multi-site multi-band configurations which are difficult to access by continuous-time Quantum Monte Carlo (CTQMC), the current leader in the field for impurity solvers for DMFT. It also could be used to strongly enhance the interaction strengths and time scales that can be studied non-equilibrium DMFT (NEQDMFT). In the second phase, these achievements are to be exploited and extended: (i) on the thematic side, we want to develop a reliable DMFT  description for vanadate compounds, for the Hubbard model in the dynamical cluster approximation (DCA) for interaction strengths hard to reach by CTQMC at zero temperature, for the phase diagram of iron pnictides, and further materials of interest as they emerge; (ii) on the methodological side, we want to study systematically improvements in the description of  the bath in order to minimize entanglement and optimize performance and describable systems, inspired by similar studies in quantum chemistry based on matrix-product states, and improvements in a crucial, but difficult bath-fitting procedure in the DMFT cycle.