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

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 calculations. In particular, the considered quenched disorder has a tunable parameter 0≤p≤1 which can be considered as a measure of randomness. Interestingly, when the magnitude of p increases from 0 to 0.95, at the associated quantum phase transitions the numerical value of the correlation length exponent ν 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, ν can reach an outcome between 0.7112(5) and 1 (or greater). Furthermore, among the studied values of p, all the associated ν violate the Harris criterion except the ones 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 an idea similar to the one used in this study. This is indeed the case according to our preliminary results stemming from investigating another disorder distribution.