# The influence of nonlocal interactions on valence transitions and formation of excitonic bound states in the generalized Falicov-Kimball model

## TL;DR

This study uses DMRG to explore how nonlocal interactions influence valence transitions and excitonic bound state formation in a generalized Falicov-Kimball model, revealing contrasting effects of different interactions.

## Contribution

It demonstrates the distinct impacts of nonlocal Coulomb interaction and correlated hopping on valence states and exciton condensation, highlighting their combined effects.

## Key findings

- $U_{nn}$ suppresses zero-momentum exciton condensation.
- $U_{ch}$ enhances exciton formation at zero momentum.
- Combined interactions cause discontinuous changes in ground-state properties.

## Abstract

We use the density-matrix-renormalization-group (DMRG) method to study the combined effects of nonlocal interactions on valence transitions and the formation of excitonic bound states in the generalized Falicov-Kimball model. In particular, we consider the nearest-neighbour Coulomb interaction $U_{nn}$ between two $d$, two $f$, $d$ and $f$ electrons as well as the so-called correlated hopping term $U_{ch}$ and examine their effects on the density of conduction $n_d$ (valence $n_f$) electrons and the excitonic momentum distribution $N(q)$. It is shown that $U_{nn}$ and $U_{ch}$ exhibit very strong and fully different effects on valence transitions and the formation (condensation) of excitonic bound states. While the nonlocal interaction $U_{nn}$ suppresses the formation of zero momentum condensate ($N(q$=$0)$) and stabilizes the intermediate valence phases with $n_d \sim 0.5, n_f \sim 0.5$, the correlated hopping term $U_{ch}$ significantly enhances the number of excitons in the zero-momentum condensate and suppresses the stability region of intermediate valence phases. The physically most interesting results are observed if both $U_{nn}$ and $U_{ch}$ are nonzero, when the combined effects of $U_{nn}$ and $U_{ch}$ are able to generate discontinuous changes in $n_f$, $N(q$=$0)$ and some other ground-state quantities.