Strong-to-Weak Spontaneous Symmetry Breaking in a $(2+1)$D Transverse-Field Ising Model under Decoherence

• URL: http://arxiv.org/abs/2603.24342v1
• Date: Wed, 25 Mar 2026 14:22:00 GMT
• Title: Strong-to-Weak Spontaneous Symmetry Breaking in a $(2+1)$D Transverse-Field Ising Model under Decoherence
• Abstract summary: We show that the decohered state realizes a rich mixed-state phase diagram governed by an effective 2D Ashkin-Teller theory.<n>This theory enables universality predictions for the mixed-state phases and the universality classes of the phase boundaries.
• Score: 10.262517965308058
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decoherence in many-body quantum systems can give rise to intrinsically mixed-state phases and phase transitions beyond the pure-state paradigm. Here we study the $(2+1)$D transverse-field Ising model subject to a strongly $\mathbb{Z}_2$-symmetric decoherence channel, with a focus on strong-to-weak spontaneous symmetry breaking (SWSSB). This problem is challenging because the relevant transitions occur in the strong-decoherence regime, beyond the reach of perturbative expansions around the pure-state limit, while conventional quantum Monte Carlo (QMC) methods are hampered by the need to access nonlinear observables and by the sign problem. We overcome these difficulties by developing a QMC algorithm that efficiently evaluates nonlinear Rényi-2 correlators in higher dimensions, complemented by an effective field-theoretic approach. We show that the decohered state realizes a rich mixed-state phase diagram governed by an effective 2D Ashkin-Teller theory. This theory enables analytical predictions for the mixed-state phases and the universality classes of the phase boundaries, all of which are confirmed by large-scale QMC simulations.

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