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Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
Hongchao Li1, Xie-Hang Yu2,3, Masaya Nakagawa1
1Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan.
Abstract:
Yang and Lee investigated phase transitions in terms of zeros of partition functions, namely, Yang-Lee zeros [Phys. Rev. 87, 404 (1952)PHRVAO0031-899X10.1103/PhysRev.87.404; Phys. Rev. 87, 410 (1952)PHRVAO0031-899X10.1103/PhysRev.87.410]. 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.
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