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<p>Symmetry plays a fundamental role in quantum many-body physics, and a central concept is spontaneous symmetry breaking. Recent developments highlight new symmetry-breaking patterns known as strong-to-weak spontaneous symmetry breaking, characterized by two different order parameters: the fidelity correlator and the Rényi-2 correlator which are inequivalent. In this work, we propose the Wightman correlator as an alternative diagnostic tool. This construction relies on the introduction of the thermofield double state for a generic density matrix, which maps the strong symmetry of the density matrix to the doubled symmetry of the pure state, allowing the Wightman correlator to emerge naturally as a standard probe of symmetry breaking. We prove the equivalence between the Wightman correlator and the fidelity correlator, and examine explicit examples. Additionally, we discuss a susceptibility interpretation of the Wightman correlator. The validity of Wightman correlator has wide applications for understanding strong-to-weak spontaneous symmetry breaking.</p>

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Diagnosing strong-to-weak symmetry breaking via Wightman correlators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月2日

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  • Zeyu Liu,
  • Langxuan Chen,
  • Yuke Zhang,
  • Shuyan Zhou,
  • Pengfei Zhang

摘要

Symmetry plays a fundamental role in quantum many-body physics, and a central concept is spontaneous symmetry breaking. Recent developments highlight new symmetry-breaking patterns known as strong-to-weak spontaneous symmetry breaking, characterized by two different order parameters: the fidelity correlator and the Rényi-2 correlator which are inequivalent. In this work, we propose the Wightman correlator as an alternative diagnostic tool. This construction relies on the introduction of the thermofield double state for a generic density matrix, which maps the strong symmetry of the density matrix to the doubled symmetry of the pure state, allowing the Wightman correlator to emerge naturally as a standard probe of symmetry breaking. We prove the equivalence between the Wightman correlator and the fidelity correlator, and examine explicit examples. Additionally, we discuss a susceptibility interpretation of the Wightman correlator. The validity of Wightman correlator has wide applications for understanding strong-to-weak spontaneous symmetry breaking.