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

Abstract

In the binary alloy with composition ${A}_{x}{B}_{1\ensuremath{-}x}$ of two atoms with ionic energy scales $\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\Delta}}$, an apparent Anderson 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 manifestly 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. The randomness takes advantage of such suppression and localizes the quasiparticles of the metallic phase. The ultimate destiny of the system at very large $U$ is to become a Mott insulator. We construct the phase diagram of this model in the plane of $(U,\mathrm{\ensuremath{\Delta}})$ for various compositions $x$.