Numerical Study of a Two-Dimensional Quantum Antiferromagnet with Random Ferromagnetic Bonds

TL;DR

This paper introduces a Monte Carlo approach for studying 2D quantum antiferromagnets with random ferromagnetic bonds, effectively reducing the sign problem and analyzing the impact of low ferromagnetic bond concentrations on antiferromagnetic order.

Contribution

A novel Monte Carlo scheme with an analytic summation over randomness that accurately studies frustrated quantum spin systems with low ferromagnetic bond concentrations.

Findings

The approximation is highly accurate up to 10% ferromagnetic bonds.

The method significantly alleviates the sign problem in simulations.

Low concentrations of ferromagnetic bonds influence antiferromagnetic properties.

Abstract

A Monte Carlo method for finite-temperature studies of the two-dimensional quantum Heisenberg antiferromagnet with random ferromagnetic bonds is presented. The scheme is based on an approximation which allows for an analytic summation over the realizations of the randomness, thereby significantly alleviating the ``sign problem'' for this frustrated spin system. The approximation is shown to be very accurate for ferromagnetic bond concentrations of up to ten percent. The effects of a low concentration of ferromagnetic bonds on the antiferromagnetism are discussed.