Dynamical mean-field theory of correlated hopping: A rigorous local approach

TL;DR

This paper develops a local dynamical mean-field theory for correlated hopping in infinite dimensions, enabling thermodynamic calculations without self-energy, and connects it to existing models and approximations.

Contribution

It introduces a rigorous local approach for correlated hopping that avoids self-energy and applies to models like Falicov--Kimball and diluted conductors.

Findings

Derived a grand-canonical potential functional for correlated hopping.

Established connections with the Blackman-Esterling-Berk CPA approach.

Analyzed limiting cases of the models with correlated hopping.

Abstract

A general approach for the description of correlated hopping in infinite dimensions, which is based on an expansion over electron hopping around the atomic limit, is developed. Such an approach keeps the dynamical mean-field theory local ideology and allows one to calculate the thermodynamical functions. A grand-canonical potential functional and a $\Phi$-derivatible theory that does not introduce the self-energy is proposed. As limiting cases the Falicov--Kimball model with correlated hopping and the model with broken bonds ("diluted" conductor) are investigated, and the connection with the Blackman-Esterling-Berk coherent potential approximation approach in the theory of the binary alloy with off-diagonal disorder is considered.