Collective excitation spectrum of a disordered Hubbard model

TL;DR

This paper investigates the collective excitation spectrum of a disordered three-dimensional Hubbard model at half-filling, revealing persistent spin-wave-like excitations despite disorder and providing microscopic insights into their localization and evolution.

Contribution

It introduces a detailed analysis of low-frequency collective excitations in a disordered Hubbard model using RPA on UHF ground states, highlighting the persistence of spin-wave-like modes.

Findings

Spin-wave-like excitations persist over a wide disorder range.

Disorder leads to localization related to local moments.

The spectrum evolution correlates with local moment distribution.

Abstract

We study the collective excitation spectrum of a d=3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder-interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.