KMS quantum symmetric states

TL;DR

This paper characterizes quantum symmetric KMS states on free product C*-algebras, showing they form a Choquet simplex and describing their extreme points, advancing understanding of quantum symmetries in operator algebras.

Contribution

It provides a complete characterization of quantum symmetric KMS states on free product C*-algebras and describes their geometric structure.

Findings

QSS_σ(A) is a nonempty Choquet simplex when it exists.

Extreme points of QSS_σ(A) are characterized.

The structure of quantum symmetric KMS states is fully described.

Abstract

Let $A$ be a unital C$^*$-algebra and let $\sigma$ be a one-parameter automorphism group of $A$. We consider $\operatorname{QSS}_\sigma(A)$, the set of all quantum symmetric states on $*_1^\infty A$ that are also KMS states (for a fixed inverse temperature, for specificity taken to be $-1$) for the free product automorphism group $*_1^\infty\sigma$. We characterize the elements of $\operatorname{QSS}_\sigma(A)$, we show that $\operatorname{QSS}_\sigma(A)$ is a Choquet simplex whenever it is nonempty and we characterize its extreme points.