Analysis of entropy of XY Spin Chain

TL;DR

This paper investigates the von Neumann entropy of a spin block in the XY model, revealing how it approaches a constant in a specific limit and varies with anisotropy and magnetic field, highlighting minima at product states and divergence at phase transitions.

Contribution

It provides a detailed analysis of the entropy behavior in the XY spin chain under a double scaling limit, connecting entropy to phase transitions and system parameters.

Findings

Entropy approaches a constant in the double scaling limit.

Entropy reaches minima at product states.

Entropy diverges at phase transitions.

Abstract

Entanglement in the ground state of the XY model on the infinite chain can be measured by the von Neumann entropy of a block of neighboring spins. We study a double scaling limit: the size of the block is much larger then 1 but much smaller then the length of the whole chain. In this limit, the entropy of the block approaches a constant. The limiting entropy is a function of the anisotropy and of the magnetic field. The entropy reaches minima at product states and increases boundlessly at phase transitions.