Thermal state entanglement entropy on a quantum graph

TL;DR

This paper explores the relationship between a particle's entanglement entropy with a spin network on a quantum graph and the graph's cycle basis, revealing connections to string-net structures in spin liquids.

Contribution

It introduces a novel link between entanglement entropy and graph cycle bases, and relates thermal states to string-net models in spin liquids.

Findings

Entanglement entropy correlates with the minimum cycle basis length.

Thermal state structure resembles string-net configurations.

Provides insights into quantum graph entanglement properties.

Abstract

A particle jumps between the nodes of a graph interacting with local spins. We show that the entanglement entropy of the particle with the spin network is related to the length of the minimum cycle basis. The structure of the thermal state is reminiscent to the string-net of spin liquids.