Self-consistent cluster CPA methods and the nested CPA theory

TL;DR

This paper develops and compares advanced cluster CPA methods, including a nested CPA approach, to accurately model disordered electronic systems in higher dimensions, addressing non-analyticities and short-range correlations.

Contribution

It introduces a nested CPA method for treating diagonal and non-diagonal disorder in higher-dimensional lattices, improving upon existing cluster CPA techniques.

Findings

Electronic structure results for Hubbard models on square and cubic lattices.

Comparison shows the nested CPA provides more consistent results.

Methods effectively incorporate short-range correlations and disorder types.

Abstract

The coherent potential approximation, CPA, is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short range correlations. In this framework one can also treat simultaneously diagonal disorder (in the site-diagonal elements of the Hamiltonian) and non-diagonal disorder (in the bond energies). It proves difficult to obtain reasonable results, free of non-analyticities, for lattices of dimension higher than one (D>1). We show electronic structure results obtained for a Hubbard model, treated in mean field approximation, on a square lattice and a simple cubic lattice, with the simultaneous inclusion of diagonal and non-diagonal disorder. We compare the results obtained using three different methods to treat the problem: a self-consistent 2-site cluster CPA method, the Blackman-Esterling-Berk single-site like extension of the CPA and a nested CPA approach.