Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity

Abstract

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.

5pages, 1 figure+14 pages, 5 figures

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• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Dissipative Superfluidity in a Molecular Bose-Einstein Condensate
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain