Spectral and Phase Structure of a Unitary Matrix Model with Fisher-Hartwig Singularities

TL;DR

This paper studies a unitary matrix model with Fisher-Hartwig singularities, revealing finite-N phase transitions and large-N third-order transitions, characterized by singularity locations and phase structure.

Contribution

It introduces a detailed analysis of phase transitions in a unitary matrix model with Fisher-Hartwig singularities, including finite-N and large-N behaviors.

Findings

Finite-N phase transitions depend on coupling.

Large-N transitions are third-order Gross-Witten-Wadia types.

Phase structure is characterized by Fisher-Hartwig singularity locations.

Abstract

We investigate a unitary matrix model with a complex potential with Fisher-Hartwig singularities. We show that the model exhibits finite-$N$ phase transitions. The order of the phase transition is coupling-dependent. At large-$N$, these transitions are replaced by third-order Gross-Witten-Wadia transitions between multiple ungapped phases and a single gapped phase, with transitions between ungapped phases forbidden. At both finite and large $N$, the phases are characterized by the locations of the Fisher-Hartwig singularities in the complex plane.