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  • Open Access

Quantum Strong-To-Weak Spontaneous Symmetry Breaking in Decohered One-Dimensional Critical States

Yuxuan Guo (郭雨轩)1,*, Sheng Yang (杨圣)2,*, and Xue-Jia Yu (余雪佳)3,4,†

  • *The first two authors contributed equally.
  • †Contact author: xuejiayu@fzu.edu.cn
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PRX Quantum 6, 040311 – Published 16 October, 2025

DOI: https://doi.org/10.1103/4vs5-l54f

Abstract

Symmetry breaking has been a central theme in classifying quantum phases and phase transitions. Recently, this concept has been extended to the mixed states of open systems, attracting considerable attention due to the emergence of novel physics beyond closed systems. In this work, we reveal a new type of phase transition in mixed states, termed quantum strong-to-weak spontaneous symmetry breaking (SWSSB). Using a combination of field theory calculations and large-scale matrix product state simulations, we map out the global phase diagram of the XXZ critical spin chain under local strong symmetry preserving decoherence, which features an SWSSB phase and a trivial Luttinger liquid phase, separated by a straight critical line that belongs to the boundary Berezinskii-Kosterlitz-Thouless universality class with a varying effective central charge. Importantly, we analyze this transition from two complementary perspectives: on one hand, through the behavior of order parameters that characterize the symmetry breaking; on the other hand, from a quantum information viewpoint by studying entropic quantities and the concept of quantum recoverability. This dual approach allows us to provide a more comprehensive understanding of the phase structure and the nature of the transition. Remarkably, the SWSSB transition in our case is purely quantum in the sense that it can only be driven by tuning the Hamiltonian parameter even under arbitrary decoherence strength, fundamentally distinguishing it from the decoherence-driven SWSSB transitions extensively discussed in previous literature. Importantly, our unified theoretical framework is applicable to a broad class of one-dimensional quantum systems, including spin chains and fermionic systems, whose low-energy physics can be described by Luttinger liquid theory, under arbitrary symmetry-preserving decoherence channels. Finally, we also discuss the experimental relevance of our theory on quantum simulator platforms.

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Popular Summary

Symmetry is a unifying principle of modern physics, underpinning phenomena from crystal formation to the Higgs mechanism in particle physics. In idealized, isolated systems this process is well understood—but real quantum devices are never perfectly closed. They are subject to decoherence, the loss of quantum coherence caused by interaction with the environment, which produces mixed quantum states. This raises a fundamental question: can symmetry-breaking phase transitions survive in such “open” quantum systems, and if so, in what new forms?

In our work, we uncover a novel kind of quantum phase transition in a one-dimensional critical spin chain exposed to symmetry-preserving decoherence. We identify a phenomenon we call quantum strong-to-weak spontaneous symmetry breaking (SWSSB). Here, the system retains only a weaker form of its global symmetry after decoherence—not because the noise strength is increased, but purely because a Hamiltonian parameter is tuned. Remarkably, this transition is insensitive to the details or strength of the environment-system coupling and has no counterpart in the noiseless limit. Our combined field theoretical analysis and large-scale numerical simulations reveal that this SWSSB transition belongs to a boundary Berezinskii-Kosterlitz-Thouless universality class.

These results deepen our understanding of quantum criticality in realistic, noisy settings and provide a guideline for probing new symmetry-breaking patterns on quantum simulators and engineered devices. By showing that such exotic transitions can occur without fine-tuning the noise, our work opens promising paths toward exploring robust quantum phenomena in inherently open systems.

Article Text

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PRX Quantum 6, 040311– Published 16 October, 2025
  • Received 24 March 2025
  • Revised 2 July 2025
  • Accepted 9 September 2025
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