Validity of Harris criterion for two-dimensional quantum spin systems with quenched disorder

TL;DR

This study uses quantum Monte Carlo simulations to examine how quenched disorder affects the critical behavior of a 2D quantum spin system, revealing that the Harris criterion's validity depends on the disorder strength.

Contribution

It provides new insights into the validity of the Harris criterion in disordered quantum spin systems, showing how the correlation length exponent varies with disorder strength.

Findings

Correlation length exponent increases with disorder parameter p

Most disorder levels violate the Harris criterion

Harris criterion remains valid only at high disorder (p=0.9)

Abstract

Inspired by the recent results regarding whether the Harris criterion is valid for quantum spin systems, we have simulated a two-dimensional spin-1/2 Heisenberg model on the square lattice with a specific kind of quenched disorder using the quantum Monte Carlo (QMC) calculations. In particular, the considered quenched disorder has a tunable parameter $0\le p \le 1$ which can be considered as a measure of randomness. Interestingly, when the magnitude of $p$ increases from 0 to 0.9, at the associated quantum phase transitions the numerical value of the correlation length exponent $\nu$ grows from a number compatible with the $O(3)$ result 0.7112(5) to a number slightly greater than 1. In other words, by varying $p$, $\nu$ can reach an outcome between 0.7112(5) and 1 (or greater). Furthermore, among the studied values of $p$, all the associated $\nu$ violate the Harris criterion except the one corresponding to $p=0.9$. Considering the form of the employed disorder here, the above described scenario should remain true for other randomness if it is based on the similar idea as the one used in this study. This is indeed confirmed by our preliminary results stemming from investigating another disorder distribution.