Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory

TL;DR

This paper develops an exact mapping from nonequilibrium DMFT to a time-dependent SIAM, enabling numerical solutions via exact diagonalization, and demonstrates its application to the Hubbard model with a focus on nonequilibrium dynamics.

Contribution

It introduces a general method to represent nonequilibrium DMFT actions as SIAMs with time-dependent parameters, facilitating numerical analysis.

Findings

Successfully mapped nonequilibrium DMFT to SIAM with time-dependent parameters

Demonstrated numerical solution using exact diagonalization techniques

Applied method to study Hubbard model dynamics after switching on hopping

Abstract

We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.