Generalized stochastic spin-wave theory for open quantum spin systems

TL;DR

This paper introduces a semiclassical spin-wave framework for simulating open quantum spin systems, capturing complex dynamics beyond traditional methods, and reveals how dissipation direction influences phase transitions.

Contribution

It develops a generalized spin-wave approach for open quantum systems, applicable to regimes with short-range interactions and local jumps, enabling large-scale simulations.

Findings

Identified a continuous phase transition with Z2 symmetry breaking when dissipation is along the drive axis.

Showed that changing interaction range affects the universality class of the criticality.

Demonstrated first-order transition when dissipation acts along the interaction axis.

Abstract

We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master equation, and generically applies to regimes beyond the reach of conventional spin-wave theories, including short-range interactions and local quantum jumps, enabling the efficient simulation of large-scale interacting spins. We illustrate the versatility of our framework by studying a variable-range driven-dissipative Ising model on a 2D lattice. When the dissipation acts along the drive axis, we find a continuous phase transition breaking the $\mathbb{Z}_2$ symmetry, and demonstrate that the interaction range, when tuned from fully-connected to nearest-neighbour, profoundly alters the universality class of the criticality. With the dissipation along the interaction axis, we show the emergence of a first-order transition. Demonstrated with both state-diffusion and quantum-jump types of trajectory dynamics, our framework provides a powerful toolbox for the efficient semiclassical description of non-equilibrium dynamics and many-body phases in spin systems.