Unitary Matrix Models with a topological term and discrete time Toda equation

TL;DR

This paper investigates full unitary matrix models incorporating a topological term and a discrete time parameter, revealing phase transitions and ground state characterizations linked to topological and instanton-like properties.

Contribution

It introduces a novel discrete time parameter in unitary matrix models and explores the effects of a topological term on phase transitions and ground states.

Findings

Phase transition at θ=π in the continuous limit

Discrete time l acts as an instanton number

Ground state characterized by the discrete time l

Abstract

We study the full unitary matrix models. Introducing a new term $l log U$, l plays the role of the discrete time. On the other hand, the full unitary matrix model contains a topological term. In the continuous limit it gives rise to a phase transition at $\theta=\pi$. The ground state is characterize by the discrete time l. The discrete time l plays like the instanton number.