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

TL;DR

This paper investigates the phase transitions in a 2+1D transverse-field Ising model under strong decoherence, revealing a rich mixed-state phase diagram and universality classes through advanced QMC methods and effective field theory.

Contribution

It introduces a novel QMC algorithm for nonlinear correlators in higher dimensions and applies it to analyze mixed-state phases under decoherence, extending understanding beyond pure states.

Findings

Identification of a rich mixed-state phase diagram governed by an effective 2D Ashkin-Teller theory

Analytical predictions of phase boundaries and universality classes confirmed by large-scale simulations

Development of an efficient QMC method for nonlinear Rènyi-2 correlators in higher dimensions

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 R\'enyi-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.