# Excitonic Insulator State of the Extended Falicov-Kimball Model in the Cluster Dynamical Impurity Approximation

## TL;DR

This study investigates the excitonic insulator phase in the extended Falicov-Kimball model on a 2D lattice using advanced cluster methods, highlighting the importance of particle-number fluctuations in understanding excitonic condensation.

## Contribution

It introduces the use of the cluster dynamical impurity approximation (CDIA) for analyzing excitonic insulators, emphasizing the role of particle-bath sites in capturing fluctuations.

## Key findings

- Demonstrates the effectiveness of CDIA in studying excitonic states.
- Provides detailed phase diagrams and order parameters.
- Shows the significance of particle-number fluctuations in excitonic condensation.

## Abstract

We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM.