Variational Dynamics of Open Quantum Spin Systems in Phase Space

TL;DR

This paper presents a variational phase-space method for simulating open quantum spin systems, accurately capturing quantum correlations and scalable to large 2D lattices.

Contribution

It introduces a novel variational approach using a mixture of spin-coherent states with negative coefficients to model quantum dynamics beyond semiclassical limits.

Findings

Accurately reproduces quantum dynamics and steady states of the quantum Ising model.

Efficiently scales to large two-dimensional lattices.

Matches results from exact diagonalization.

Abstract

We introduce a variational method for simulating the dynamics of interacting open quantum spin systems. The method is based on the spin phase-space representation and variationally targets the Husimi-$Q$ function with an ansatz based on a multi-dimensional mixture of spin-coherent states. Crucially, the mixture coefficients are allowed to take negative values, enabling the faithful capture of quantum correlations beyond semiclassical descriptions. The resulting equations of motion are derived from the Dirac-Frenkel variational principle and can be evaluated efficiently without resorting to Monte Carlo sampling by exploiting the analytical structure of the ansatz. As a first application, we demonstrate that this approach accurately captures both the full quantum dynamics and the non-equilibrium steady states of the transverse-field quantum Ising model, in excellent agreement with exact diagonalization. Furthermore, we show that the method scales efficiently to large two-dimensional lattices, a regime that remains challenging for other techniques.