Exact quantum dynamics of Fermi--Hubbard systems using the Gaussian phase-space representation with diffusion gauges

TL;DR

This paper presents an improved Gaussian phase-space method with diffusion gauges for simulating the real-time dynamics of interacting fermions in multiple dimensions, extending the practical simulation time and system size.

Contribution

The authors develop an efficient algorithm to optimize diffusion gauges, significantly enhancing the Gaussian phase-space representation's applicability to larger and longer simulations of Fermi-Hubbard systems.

Findings

Extended simulation time by optimizing diffusion gauges.

Applicable to larger, more complex Fermi-Hubbard systems.

Achieved more accurate real-time dynamics of interacting fermions.

Abstract

We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The spiking can be delayed, and the practical simulation time extended, by adjusting the gauges of the representation, resulting in different equivalent stochastic differential equations. Here, we work on the so-called diffusion gauge and propose an algorithm to find efficiently new implementations of the noise terms. Compared with our initial results [F. Rousse \textit{et al.} 2024, J. Phys. A: Math. Theor. \textbf{57}, 015303], the new method achieves a significantly longer practical simulation time and can be applied to significantly larger systems.