Random-exchange quantum Heisenberg antiferromagnets on the square lattice

TL;DR

This study investigates the robustness of antiferromagnetic order in two-dimensional quantum Heisenberg models with random exchange interactions, finding that long-range order persists despite strong disorder, unlike in one dimension.

Contribution

It provides a comprehensive analysis combining multiple computational methods to show that 2D antiferromagnetic order is resilient against strong randomness, contrasting with 1D behavior.

Findings

Long-range order remains stable under strong disorder in 2D.

Antiferromagnetic order parameter decreases exponentially with disorder strength.

Order vanishes only at infinite randomness.

Abstract

The ground state properties of random-exchange spin-1/2 Heisenberg antiferromagnets on the square lattice are investigated using a combination of quantum Monte Carlo simulations, exact numerical diagonalizations, and spin wave calculations. Whereas arbirarily weak disorder has a drastic effect on 1d Heisenberg AFM, we find that in two dimensions the characteristics of the ground state like long-range order is robust even against strong disorder. While the antiferromagnetic order parameter and the spin stiffness are exponentially reduced for singular exchange distributions, they vanish only in the limit of infinite randomness.