论文标题
Yang-Lee零，半圆定理和Bardeen-Cooper-Schrieffer超导性的非单身关键性
Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
论文作者
论文摘要
杨和李根据分区函数的零，即杨李零[Phys。 Rev. 87，404（1952）;物理。修订版87，410（1952）]。我们表明，超导间隙的基本奇异性与BCS超导体的分区函数的根数直接相关。由于费米 - 表面不稳定性，发现这些零在相互作用强度的复杂平面上分布在半圆形上。重新归一化组分析表明，半圆定理具有具有边缘耦合的通用量子多体系统，与Ising自旋系统的Lee-Yang Circle定理形成鲜明对比。这表明Yang-Lee零的几何形状直接连接到Fermi-Surface的不稳定性。此外，我们揭示了BCS超导性的单身关键性，由于特殊点，每个单个Yang-Lee零都会出现，并提出了与常规Yang-Lee边缘奇异性不同的普遍性类别。
Yang and Lee investigated phase transitions in terms of zeros of partition functions, namely, Yang-Lee zeros [Phys. Rev. 87, 404 (1952); Phys. Rev. 87, 410 (1952)]. We show that the essential singularity in the superconducting gap is directly related to the number of roots of the partition function of a BCS superconductor. Those zeros are found to be distributed on a semicircle in the complex plane of the interaction strength due to the Fermi-surface instability. A renormalization-group analysis shows that the semicircle theorem holds for a generic quantum many-body system with a marginal coupling, in sharp contrast with the Lee-Yang circle theorem for the Ising spin system. This indicates that the geometry of Yang-Lee zeros is directly connected to the Fermi-surface instability. Furthermore, we unveil the nonunitary criticality in BCS superconductivity that emerges at each individual Yang-Lee zero due to exceptional points and presents a universality class distinct from that of the conventional Yang-Lee edge singularity.
