Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution

TL;DR

This study uses strong disorder renormalization group techniques to analyze the low-energy properties of disordered S=1/2 Heisenberg antiferromagnetic layers and bilayers, revealing phase boundaries, critical exponents, and the effects of different disorder types.

Contribution

It provides a detailed numerical analysis of how bond randomness, site, and dimer dilution influence the phases and critical behavior of quantum antiferromagnets, including the role of disorder strength.

Findings

Critical exponents are independent of bond randomness in the strong disorder regime.

Dynamical exponent varies continuously with disorder strength.

Quantum Monte Carlo results support the renormalization group analysis.

Abstract

Using a numerical implementation of strong disorder renormalization group, we study the low-energy, long-distance properties of layers and bilayers of $S = 1/2$ Heisenberg antiferromagnets with different type of disorder: bond randomness, site and dimer dilution. Generally the systems exhibit an ordered and a disordered phase separated by a phase boundary on which the static critical exponents appear to be independent of bond randomness in the strong disorder regime, while the dynamical exponent is a continuous function of the bond disorder strength. The low-energy fixed points of the off-critical phases are affected by the actual form of the disorder, and the disorder induced dynamical exponent depends on the disorder strength. As the strength of bond disorder is increased, there is a set of crossovers in the properties of the low-energy singularities. For weak disorder quantum fluctuations play the dominant role. For intermediate disorder non-localized disorder fluctuations are relevant, which become localized for even stronger bond disorder. We also present some quantum Monte Carlo simulations results to support the strong disorder renormalization approach.