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 ℤ2-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 α≈ 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.
Related
- Non-Equilibrium Instantaneous Approximation and Dipole Forbidden d-d Transitions
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BibTeX
@misc{timofeev2026systematic,
title = {{Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium}},
author = {Igor Timofeev and Dawid A. Hryniuk and Marzena H. Szymańska},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27462},
eprint = {2610.27462},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27462},
}
RIS
TY - UNPB
TI - Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium
AU - Igor Timofeev
AU - Dawid A. Hryniuk
AU - Marzena H. Szymańska
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27462
UR - https://arxiv.org/abs/2610.27462
AB - 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 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 α≈ 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.
ER -