Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems

TL;DR

This paper introduces an efficient phase-space numerical method for simulating large collective spin systems with dissipation, enabling analysis of complex non-equilibrium phenomena beyond traditional approaches.

Contribution

It extends the truncated Wigner approximation using Schwinger bosons to accurately simulate dissipative spin dynamics in large systems.

Findings

Effective for large spin quantum numbers

Accurately reproduces superradiant decay

Simulates non-equilibrium phase transitions

Abstract

We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.