Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium

Abstract:Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin $S$. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended $\mathbb{Z}_2$-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond $\alpha\approx 3.5$. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)

arXiv:2610.27462 [quant-ph]

(or arXiv:2610.27462v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.27462 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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