Correlated hopping in the Falicov-Kimball model: A large-dimensions study

TL;DR

This paper investigates the effects of correlated hopping in the Falicov-Kimball model using an extended dynamical mean-field theory in large dimensions, revealing significant nonlocal dynamical contributions.

Contribution

It introduces an exact large-dimensional solution for the model with correlated hopping, highlighting the importance of nonlocal correlations often neglected in simpler models.

Findings

Correlated hopping induces nonlocal self-energy components.

Nonlocal dynamical effects are significant at large hopping amplitudes.

Neglecting correlated hopping omits important nonlocal correlations.

Abstract

The Falicov-Kimball model with a correlated-hopping interaction is solved using an extended dynamical mean-field theory that becomes exact in the limit of large dimensions. The effect of correlated hopping is to introduce nonlocal self-energy components that retain full dynamics as D goes to infinity, thus introducing an explicit k-dependence to the single-particle self-energy. An explicit solution for the homogeneous phase at D = 2 reveals significant nonlocal dynamical contributions in the physically relevant regime of a moderately large correlated-hopping amplitude, indicating that important nonlocal correlations are omitted in Hubbard-like models upon neglecting the correlated-hopping interaction.