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

TL;DR

This study uses quantum Monte Carlo methods to analyze a disordered 2D quantum spin system, revealing how disorder affects critical exponents, energy density, and Wilson ratios, providing benchmarks for future research.

Contribution

First-principles QMC calculations of disorder effects on critical properties and energy in a 2D quantum spin system, highlighting disorder-dependent variations.

Findings

Disorder parameter p influences dynamic critical exponent z.

Wilson ratio W varies with disorder, showing complementary behavior to z.

Ground state energy density E_0 is precisely determined across disorder levels.

Abstract

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 (QMC). The employed disorder distribution has a tunable parameter $p$ which can be considered as a measure of the corresponding randomness. In particular, when $p=0$ the disordered system becomes the clean one. Through a large scale QMC, the dynamic critical exponents $z$, the ground state energy densities $E_0$, as well as the Wilson ratios $W$ of various $p$ are determined with high precision. Interestingly, we find that the $p$ dependence of $z$ and $W$ are likely to be complementary to each other. For instance, while the $z$ of $0.4 \le p \le 0.9$ match well among themselves and are statistically different from $z=1$ which corresponds to the clean system, the $W$ for $p < 0.7$ are in reasonable good agreement with that of $p=0$. The technical subtlety of calculating these physical quantities for a disordered system is demonstrated as well. The results presented here are not only interesting from a theoretical perspective, but also can serve as benchmarks for future related studies.