退相干费米子的强到弱自发对称性破缺
Strong-to-Weak Spontaneous Symmetry Breaking of Dephased Fermions
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中文总结 AI 辅助
本文研究无限退相干下U(1)对称费米子的强到弱自发对称性破缺，通过XY模型映射与图解展开揭示金属与绝缘母态的SWSSB相变及其普适类。
中文摘要 AI 辅助
强到弱自发对称性破缺（SWSSB）是混合态中一种新颖的相变，与全局电荷信息的丢失相关。在这项工作中，我们研究了在无限密度退相干下具有$U(1)$对称性的费米子，并推导了由此产生的混合态的SWSSB性质。我们的核心观察是，在无限退相干下，每个Renyi关联函数恰好是紧致XY模型的自旋-自旋关联函数，其玻尔兹曼权重是源自母态的经典系综的平方全计数统计生成函数。对于Renyi-2关联函数，它正是母态自身的全计数统计。我们通过一种新颖的图解展开来补充无限退相干映射，该展开适用于Renyi-1关联函数，可应用于任何对角混合态，并计算Renyi-1 XY模型的耦合常数。我们还研究了适用于有限退相干情况下偶数Renyi指数量的副本场论。我们的分析表明，完全退相干的金属在$d\geq 2$维度表现出长程SWSSB，这在$d=2$中已通过数值和实验证实，并在$d=1$中表现出准长程SWSSB。对于绝缘母态，在无限退相干下，根据紫外细节，可能同时存在SWSSB相和平庸相。当母态深处于绝缘相时，$d\geq 3$维度的长程SWSSB或$d=2$维度的准长程SWSSB会在一个非普适的、依赖于Renyi指数的阈值之上存活，但会丧失，量子霍尔绝缘体除外，它们通常具有准长程SWSSB。对于偶数Renyi指数，我们还确定了SWSSB相在偏离无限退相干时的稳定性，并推导了SWSSB转变的普适类。
英文摘要
Strong-to-weak spontaneous symmetry breaking (SWSSB) is a novel phase transition in mixed states associated with the loss of global charge information. In this work we study fermions with $U(1)$ symmetry under infinite density dephasing and derive the SWSSB properties of the resulting mixed states. Our central observation is that at infinite dephasing every Renyi correlator is exactly the spin-spin correlator of a compact XY model, whose Boltzmann weight is the squared full-counting-statistics generating function of a classical ensemble built from the parent state. For the Renyi-2 correlator it is the full counting statistics of the parent state itself. We complement the infinite dephasing mapping with a novel diagrammatic expansion for the Renyi-1 correlator, applicable to any diagonal mixed state, which computes the couplings of the Renyi-1 XY model. We also study a replica field theory for even Renyi index quantities, applicable at finite dephasing. Our analysis indicates that fully dephased metals display long-range SWSSB in $d\geq 2$, as confirmed numerically and experimentally in $d=2$, and quasi-long-range SWSSB in $d=1$. For insulating parent states both an SWSSB and a trivial phase are possible at infinite dephasing depending on UV details. Long-range SWSSB in $d\geq 3$, or quasi-long-range SWSSB in $d=2$, survives above a nonuniversal, Renyi-index-dependent threshold and is lost when the parent state is deep in the insulating phase, with the exception of quantum Hall insulators which generically have quasi-long-range SWSSB. For even Renyi indices we also determine the stability of the SWSSB phase away from infinite dephasing and derive the universality class of the SWSSB transition.
发表机构
- University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
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