Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations

TL;DR

This paper develops a self-consistent perturbation method based on the non-crossing approximation to solve the impurity problem in nonequilibrium dynamical mean-field theory for the Hubbard model, effectively capturing key physical regimes.

Contribution

It introduces a generalized perturbative approach around the atomic limit that improves upon the NCA, accurately reproducing Monte Carlo results across various regimes.

Findings

Low-order corrections to NCA match Monte Carlo results in the insulating and crossover regimes.

The method effectively describes the response of double occupancy to interaction and hopping changes.

Applicable to ultracold fermionic gases probing Mott insulators.

Abstract

We solve the impurity problem which arises within nonequilibrium dynamical mean-field theory for the Hubbard model by means of a self-consistent perturbation expansion around the atomic limit. While the lowest order, known as the non-crossing approximation (NCA), is reliable only when the interaction U is much larger than the bandwidth, low-order corrections to the NCA turn out to be sufficient to reproduce numerically exact Monte Carlo results in a wide parameter range that covers the insulating phase and the metal-insulator crossover regime at not too low temperatures. As an application of the perturbative strong-coupling impurity solver we investigate the response of the double occupancy in the Mott insulating phase of the Hubbard model to a dynamical change of the interaction or the hopping, a technique which has been used as a probe of the Mott insulating state in ultracold fermionic gases.