KMS states on quantum Cuntz-Krieger algebras

TL;DR

This paper investigates KMS states on quantum Cuntz-Krieger algebras linked to quantum graphs, translating classical criteria into the quantum setting and providing a full classification for certain gauge actions.

Contribution

It extends the classical theory of KMS states to quantum Cuntz-Krieger algebras via quantum graph isomorphisms and classifies states for specific gauge actions.

Findings

KMS states characterized by quantum adjacency operators

Complete classification for gauge actions in certain cases

Isomorphism to Cuntz-Pimsner algebras facilitates analysis

Abstract

We study the KMS states on local quantum Cuntz-Krieger algebras associated to quantum graphs. Using their isomorphism to the Cuntz-Pimsner algebra of the quantum edge correspondence, we show that the general criteria for KMS states can be translated into statements about the underlying quantum adjacency operator, somewhat analogously to the case of classical Cuntz-Krieger algebras. We study some examples of gauge actions, for which a complete classification of KMS states can be obtained.