Anderson-Hubbard Model in $d = \infty$

TL;DR

This paper investigates the interplay of interactions and disorder in the Anderson-Hubbard model at infinite dimensions, revealing a phase with antiferromagnetic order and a novel disorder-enhanced Néel temperature.

Contribution

It provides a detailed analytical and numerical study of the Anderson-Hubbard model in infinite dimensions, discovering a disorder-induced increase in the Néel temperature and complex transition scenarios.

Findings

Existence of antiferromagnetic long-range order at low temperatures and strong interactions.

Discovery of a disorder-induced increase in the Néel temperature.

Complex metal-insulator and magnetic transition scenarios depending on disorder.

Abstract

We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.