Solving nonequilibrium dynamical mean-field theory using matrix product states

TL;DR

This paper advances nonequilibrium DMFT solutions by employing matrix product states, enabling larger bath sizes and longer simulation times, with improved efficiency through star geometry and a novel hybridization function approximation.

Contribution

It introduces an MPS-based method for nonequilibrium DMFT that surpasses previous limitations in bath size and simulation duration, utilizing star geometry and a new hybridization approximation.

Findings

Longer simulation times achieved (factor 2-3) compared to exact diagonalization.

Star geometry improves entanglement properties and computational efficiency.

Approximation of hybridization function using time-translational invariance.

Abstract

We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix product states (MPS). This allows us to treat much larger bath sizes and by that reach substantially longer times (factor $\sim$ 2 -- 3) than with exact diagonalization. We show that the star geometry of the underlying impurity problem can have substantially better entanglement properties than the previously favoured chain geometry. This has immense consequences for the efficiency of an MPS-based description of general impurity problems: in the case of equilibrium DMFT, it leads to an orders-of-magnitude speedup. We introduce an approximation for the two-time hybridization function that uses time-translational invariance, which can be observed after a certain relaxation time after a quench to a time-independent Hamiltonian.