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

TL;DR

This paper links the distribution of Yang-Lee zeros in the complex interaction plane to Fermi-surface instability in BCS superconductors, revealing a semicircle distribution and nonunitary criticality with a new universality class.

Contribution

It demonstrates the semicircle distribution of Yang-Lee zeros in BCS superconductivity and uncovers nonunitary criticality associated with exceptional points, extending the Lee-Yang circle theorem.

Findings

Zeros distributed on a semicircle in the complex plane

Fermi-surface instability related to zero distribution

Nonunitary criticality at Yang-Lee zeros

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.