Phase transitions in the binary-alloy Hubbard model: insight from strong-coupling perturbation theory

TL;DR

This paper investigates phase transitions in a binary-alloy Hubbard model on a honeycomb lattice, revealing how increasing Hubbard interaction U induces transitions from Anderson insulator to metal, then back to Anderson insulator, and finally to Mott insulator, using strong-coupling perturbation theory.

Contribution

The study introduces a novel combination of local self-energy from strong-coupling perturbation theory with transfer matrix method to analyze large-scale binary-alloy Hubbard models.

Findings

Hubbard U screens disorder, inducing metallic behavior in the Anderson insulator.

Further increase in U suppresses charge fluctuations, leading to re-entrant Anderson insulating phase.

At very large U, the system transitions to a Mott insulator.

Abstract

In the binary-alloy with composition A$_x$B$_{1-x}$ of two atoms with ionic energy scales $\pm\Delta$, an apparent Ander- son insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard $U$ to the binary alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction $U$, the resulting AI phase will become metallic which in our formulation can be clearly attributed to the screening of disorder by Hubbard $U$. Upon further increase in $U$, again the AI phase emerges which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction of which the randomness takes advantage and localizes the quasi-particles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator (MI). We construct the phase diagram of this model in the plane of ($U,\Delta$) for various compositions $x$.