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

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.

Comments: 7 pages,11 figures, 8 tables