The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model

TL;DR

This study explores how next-nearest-neighbour density interactions influence phase behavior in the atomic limit of the extended Hubbard model, revealing complex phase diagrams with multiple ordered and phase-separated states.

Contribution

First analysis of longer-range density interactions in the atomic limit of the extended Hubbard model, uncovering new multicritical phenomena and phase separation behaviors.

Findings

Multiple charge-ordered phases identified

Presence of phase separation between different states

Complex multicritical points such as bicritical and tricritical points

Abstract

We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points.