Using Random Boundary Conditions to simulate disordered quantum spin models in 2D-systems

TL;DR

This paper introduces a method using random boundary conditions in exact diagonalization to identify disordered quantum antiferromagnets in 2D systems, effectively distinguishing between ordered and disordered phases.

Contribution

The authors propose a novel approach employing random boundary conditions and averaging to detect disordered phases in small lattice simulations of quantum spin models.

Findings

Successfully reproduces ordered phases of the model.

Signals disordered phases via quasi degenerate ground states and lack of local order.

Method shows weak dependence on finite size effects.

Abstract

Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both, theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizations. We apply our method to study a Heisenberg spin-1/2 model in an anisotropic triangular lattice. In this model, the competition between frustration and quantum fluctuations might lead to some spin liquid phases as predicted from different methods ranging from spin wave mean field theory to 2D-DMRG or PEPS. Our method accurately reproduces the ordered phases expected of the model and signals disordered phases by the presence of a large number of quasi degenerate ground states together with the absence of a local order parameter. The method presents a weak dependence on finite size effects.