Critical exponent in the magnetization curve of quantum spin chains

TL;DR

This paper investigates the critical behavior of the magnetization curve near the critical field in quantum spin chains, proposing a size scaling method to estimate the critical exponent, and finds a universal value of 2 across different models.

Contribution

It introduces a size scaling method to accurately estimate the critical exponent in quantum spin chains from finite cluster calculations.

Findings

Critical exponent δ = 2 for S=1 antiferromagnetic chain.

Critical exponent δ = 2 for S=1/2 bond alternating chain.

Universal δ = 2 for edges of the magnetization plateau in S=3/2 chain.

Abstract

The ground state magnetization curve around the critical magnetic field $H_c$ of quantum spin chains with the spin gap is investigated. We propose a size scaling method to estimate the critical exponent $\delta$ defined as $m\sim |H-H_c|^{1/\delta}$ from finite cluster calculation. The applications of the method to the S=1 antiferromagnetic chain and S=1/2 bond alternating chain lead to a common conclusion $\delta =2$. The same result is derived for both edges of the magnetization plateau of the S=3/2 antiferromagnetic chain with the single ion anisotropy.