Magnetic Correlations in the Two Dimensional Anderson-Hubbard Model

TL;DR

This study uses quantum Monte Carlo simulations to explore how different types of disorder affect magnetic order and electronic properties in the two-dimensional Hubbard model at half filling.

Contribution

It provides a detailed analysis of how diagonal and off-diagonal disorder influence magnetic correlations and antiferromagnetic order in the 2D Hubbard model.

Findings

Diagonal disorder suppresses local magnetic moments and destroys antiferromagnetic order.

Off-diagonal disorder does not significantly reduce local magnetic moments and allows larger lattice studies.

A disordered phase near the transition is incompressible with increased low-temperature susceptibility.

Abstract

The two dimensional Hubbard model in the presence of diagonal and off-diagonal disorder is studied at half filling with a finite temperature quantum Monte Carlo method. Magnetic correlations as well as the electronic compressibility are calculated to determine the behavior of local magnetic moments, the stability of antiferromagnetic long range order (AFLRO), and properties of the disordered phase. The existence of random potentials (diagonal or ``site'' disorder) leads to a suppression of local magnetic moments which eventually destroys AFLRO. Randomness in the hopping elements (off-diagonal disorder), on the other hand, does not significantly reduce the density of local magnetic moments. For this type of disorder, at half-filling, there is no ``sign-problem'' in the simulations as long as the hopping is restricted between neighbor sites on a bipartite lattice. This allows the study of sufficiently large lattices and low temperatures to perform a finite-size scaling analysis. For off-diagonal disorder AFLRO is eventually destroyed when the fluctuations of antiferromagnetic exchange couplings exceed a critical value. The disordered phase close to the transition appears to be incompressible and shows an increase of the uniform susceptibility at low temperatures.