Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

TL;DR

This paper introduces a Hybrid Phase-Space method combining phase-space techniques and reduced density matrices to improve the simulation of interacting fermions, demonstrating enhanced accuracy over traditional stochastic mean-field approaches.

Contribution

It develops a novel Hybrid Phase-Space approach that incorporates correlations beyond mean-field by integrating BBGKY hierarchy equations, applied to the Fermi-Hubbard model.

Findings

Improved predictive accuracy over stochastic mean-field methods.

Accurate results in the weak-coupling regime for long times.

Close agreement with exact solutions in tested scenarios.

Abstract

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where the complex dynamics of interacting fermions is replaced by a statistical average of mean-field like trajectories is able to grasp some correlations beyond the mean-field. We explore the possibility to use alternative equations of motion in the phase-space approach. Guided by the BBGKY hierarchy, equations of motion that already incorporate part of the correlations beyond mean-field are employed along each trajectory. The method is called Hybrid Phase-Space (HPS) because it mixes phase-space techniques and the time-dependent reduced density matrix approach. The novel approach is applied to the one-dimensional Fermi-Hubbard model. We show that the predictive power is improved compared to the original stochastic mean-field method. In particular, in the weak-coupling regime, the results of the HPS theory can hardly be distinguished from the exact solution even for long time.