Phase Diagram of the Two-Dimensional Anderson-Hubbard Model

TL;DR

This paper investigates the phase diagram of the two-dimensional Anderson-Hubbard model, revealing a transition from Anderson to Mott insulators at half filling and emphasizing the role of electron-electron interactions in gapless insulating phases.

Contribution

It provides the first detailed phase diagram of the 2D Anderson-Hubbard model near half filling using a quantum real space renormalization group method.

Findings

System is always insulating with disorder.

Transition from gapless to incompressible insulator at critical U.

Gapless insulating phase controlled by Anderson fixed point.

Abstract

We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction $U$ reaches a critical value $U_c$. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.