Entropy of XY Spin Chain and Block Toeplitz Determinants

TL;DR

This paper rigorously analyzes the entanglement entropy in the ground state of the infinite XY spin chain, showing its behavior at phase transitions and providing a proven expression for the limiting entropy.

Contribution

It provides a rigorous proof of the limiting entropy expression for the XY spin chain's ground state entanglement.

Findings

Entropy approaches a constant for large blocks

Entropy reaches minimum at product states

Entropy increases without bound at phase transitions

Abstract

We consider entanglement in the ground state of the XY spin model on infinite chain. We use von Neumann entropy of a sub-system as a measure of entanglement. The entropy of a large block of neighboring spins approaches a constant as the size of the block increases. We prove rigorously expression for limiting entropy which was published before. We observe that the entropy reaches minimum at product states but increases boundlessly at phase transitions.