Ground-state energy density, susceptibility, and Wilson ratio of a two-dimensional disordered quantum spin system

A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a specific kind of quenched disorder is investigated, using the first-principles nonperturbative quantum Monte Carlo calculations (QMCs). The employed disorder distribution has a tunable parameter $p$ which can be considered as a measure of randomness ($p=0$ correponds to the clean model). Through large-scale QMCs, the dynamic critical exponents $z$, the ground-state energy densities ${E}_{0}$, and the Wilson ratios $W$ of various $p$ are determined with high precision. Interestingly, we find that the $p$ dependencies of $z$ and $W$ are likely to be complementary to each other. For instance, while the $z$ values of $0.4\ensuremath{\le}p\ensuremath{\le}0.9$ match well among themselves and are statistically different from that of $p=0$, the $W$ values for $pl0.7$ are in reasonably good agreement with $W\ensuremath{\sim}0.1243$ of the clean case. Surprisingly, our study indicates that a threshold of randomness, ${p}_{W}$, associated with $W$ exists. In particular, beyond this threshold the magnitude of $W$ grows with $p$. This is somehow counterintuitive since one expects the spin correlations should diminish accordingly. Similarly, there is a threshold ${p}_{z}$ related to $z$ after which a constant value is obtained for $z$. The results presented here are not only interesting from a theoretical perspective but also can serve as benchmarks for future related studies.