Monte Carlo determination of the critical exponents for a quantum phase transition of a dimerized spin-1/2 Heisenberg model

TL;DR

This study uses Monte Carlo simulations to precisely determine critical exponents for a quantum phase transition in a dimerized spin-1/2 Heisenberg model, confirming its alignment with the O(3) universality class.

Contribution

The paper provides high-precision Monte Carlo estimates of critical exponents for the quantum phase transition, validating the universality class and improving the accuracy of known critical parameters.

Findings

Critical exponent $eta/ u$ matches known O(3) universality class value.

Confluent exponent $\omega$ is consistent with established results.

Quantum phase transition aligns with O(3) universality class.

Abstract

We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents $\beta/\nu$ and $\omega$ associated with the quantum phase transition induced by dimerization are determined with high precision. Here $\beta$ and $\nu$ are the exponents related to the magnetization and the correlation length, respectively. In addition, $\omega$ is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of $\omega$ compatible with the known result in the O(3) universality class. Further, using either the value of $\omega$ determined here or the established one in the literature, the exponent $\beta/\nu$ calculated from our data is in quantitative agreement with the known result $\beta/\nu = 0.519(1)$ as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.