Importance of realistic phase space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

TL;DR

This paper demonstrates that using a realistic phase-space representation, such as the Husimi distribution, within the stochastic mean-field approach significantly improves the modeling of initially correlated fermionic quantum systems, especially beyond Gaussian assumptions.

Contribution

The paper introduces a method combining the stochastic mean-field approach with Husimi distribution to better represent initial quantum fluctuations in correlated fermionic systems.

Findings

Gaussian phase-space assumption fails for correlated states

Husimi distribution improves initial state representation

Method achieves perfect agreement in weak coupling regime

Abstract

In the stochastic mean-field (SMF) approach, an ensemble of initial values for a selected set of one-body observables is formed by stochastic sampling from a phase-space distribution that reproduces the initial quantum fluctuations. Independent mean-field evolutions are performed with each set of initial values followed by averaging over the resulting ensemble. This approach has been recently shown to be rather versatile and accurate in describing the correlated dynamics beyond the independent particle picture. In the original formulation of SMF, it was proposed to use a Gaussian assumption for the phase-space distribution. This assumption turns out to be rather effective when the dynamics of an initially uncorrelated state is considered, which was the case in all applications of this approach up to now. Using the Lipkin-Meshkov-Glick (LMG) model, we show that such an assumption might not be adequate if the quantum system under interest is initially correlated and presents configuration mixing between several Slater determinants. In this case, a more realistic description of the initial phase-space is necessary. We show that the SMF approach can be advantageously combined with standard methods to describe phase-space in quantum mechanics. As an illustration, the Husimi distribution function is used here to obtain a realistic representation of the phase-space of a quantum many-body system. This method greatly improves the description of initially correlated fermionic many-body states. In the LMG model, while the Gaussian approximation failed to describe these systems in all interaction strength range, the novel approach gives a perfect agreement with the exact evolution in the weak coupling regime and significantly improves the description of correlated systems in the strong coupling regime.