Invariance of KMS states on graph C*-algebras under classical and quantum symmetry

TL;DR

This paper investigates how KMS states on graph C*-algebras behave under classical and quantum symmetries, revealing invariance properties and differences between strongly connected and circulant graphs.

Contribution

It demonstrates that the unique KMS state on strongly connected graphs is invariant under quantum automorphisms, and explores invariance of KMS states on circulant graphs under both classical and quantum symmetries.

Findings

Unique KMS state on strongly connected graphs is quantum invariant.

Only one KMS state at critical temperature is invariant under classical and quantum automorphisms in circulant graphs.

Existence of graphs with multiple KMS states where only one is quantum invariant.

Abstract

We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant under quantum automorphism group of the graph. For circulant graphs, it is shown that the action of classical and quantum automorphism group preserves only one of the KMS states occurring at the critical inverse temperature. We also give an example of a graph C*-algebra having more than one KMS state such that all of them are invariant under the action of classical automorphism group of the graph, but there is a unique KMS state which is invariant under the action of quantum automorphism group of the graph.