Exact relationship between the entanglement entropies of XY and quantum Ising chains

TL;DR

This paper establishes an exact relationship between the entanglement entropies of the XY and quantum Ising chains, enabling translation of known results and providing new insights into their critical properties.

Contribution

It introduces an exact formula linking the entanglement entropies of the XY and Ising models, using free-fermion and perturbation methods, advancing understanding of their quantum critical behavior.

Findings

Derived the additive constant of the entropy for the critical homogeneous Ising chain

Determined the effective central charge of the random XY chain

Established a direct relationship between the entanglement entropies of the two models

Abstract

We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.