Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium
Year: 2026
Type: preprint
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 $α\approx 3.5$. 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.
Source: arXiv (Cornell University)
Institution: University College London
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2041947046, Quantum and Many Body Physics Enabled by Advanced Semiconductor Nanotechnology, DTP 2018-19 University College London, G277190163, Modelling Center for Quantum Technologies, Far From Equilibrium Quantum Simulators, Protection of quantum information in small clusters of qubits, G7564478775, DTP 2016-2017 University College London, DTP 2020-2021 University College London
OpenAlex ID: W7223155503