Competition between disorder and Coulomb interaction in a two-dimensional plaquette Hubbard model

TL;DR

This study investigates how disorder and Coulomb interactions compete in a two-dimensional plaquette Hubbard model, revealing transitions between band insulators, Anderson insulators, correlated metals, and Mott insulators depending on disorder size and interaction strength.

Contribution

It introduces a combined CPA and DMFT approach to analyze a plaquette Hubbard model, bridging ionic and Anderson models, and explores phase transitions driven by disorder and interactions.

Findings

Band insulator behavior in small plaquettes with strong disorder.

Anderson insulator with gapless states in large plaquettes.

Emergence of correlated metallic states with increasing interaction.

Abstract

We have studied a disordered $N_{\rm c} \times N_{\rm c}$ plaquette Hubbard model on a two-dimensional square lattice at half-filling using a coherent potential approximation (CPA) in combination with a single-site dynamical mean field theory (DMFT) approach with a paramagnetic bath. Such a model conveniently interpolates between the ionic Hubbard model at $N_{\rm c}=\sqrt{2}$ and the Anderson model at $N_{\rm c} = \infty$ and enables the analysis of the various limiting properties. We confirmed that within the CPA approach a band insulator behavior appears for non-interacting strongly disordered systems with a small plaquette size $N_{\rm c} = 4$, while the paramagnetic Anderson insulator with nearly gapless density of states is present for large plaquette sizes $N_{\rm c}=48$. When the interaction $U$ is turned on in the strongly fluctuating random potential regions, the electrons on the low energy states push each other into high energy states in DMFT in a paramagnetic bath and correlated metallic states with a quasiparticle peak and Hubbard bands emerge, though a larger critical interaction $U$ is needed to obtain this state from the paramagnetic Anderson insulator ($N_{\rm c}=48$) than from the band insulator ($N_{\rm c}=4$). Finally, we observe a Mott insulator behavior in the strong interaction $U$ regions for both $N_{\rm c}=4$ and $N_{\rm c}=48$ independent of the disorder strength. We discuss the application of this model to real materials.