Entanglement entropy scaling of the XXZ chain

TL;DR

This paper investigates how entanglement entropy scaling in the XXZ chain is affected by the ferromagnetic point, revealing crossover effects that influence the estimation of the central charge and related critical properties.

Contribution

It provides a detailed analysis of entanglement entropy scaling at the ferromagnetic point and its impact on accurately estimating the central charge in the XXZ chain.

Findings

Entanglement entropy scales logarithmically at the ferromagnetic point with a different coefficient.

Crossover behavior affects the estimation of the central charge and other critical parameters.

Methods for distinguishing genuine critical behavior from crossover effects are discussed.

Abstract

We study the entanglement entropy scaling of the XXZ chain. While in the critical XY phase of the XXZ chain the entanglement entropy scales logarithmically with a coefficient that is determined by the associated conformal field theory, at the ferromagnetic point, however, the system is not conformally invariant yet the entanglement entropy still scales logarithmically albeit with a different coefficient. We investigate how such an nontrivial scaling at the ferromagnetic point influences the estimation of the central charge $c$ in the critical XY phase. In particular we use the entanglement scaling of the finite or infinite system, as well as the finite-size scaling of the ground state energy to estimate the value of $c$. In addition, the spin-wave velocity and the scaling dimension are also estimated. We show that in all methods the evaluations are influenced by the nearby ferromagnetic point and result in crossover behavior. Finally we discuss how to determine whether the central charge estimation is strongly influenced by the crossover behavior and how to properly evaluate the central charge.