Charge-Ordered States and the Phase Diagram of the Extended Hubbard Model on the Bethe lattice

TL;DR

This paper investigates the phase diagram of the extended Hubbard model on the Bethe lattice, revealing various charge-ordered and metallic states, and analyzing how interactions influence these phases at finite temperatures.

Contribution

It provides analytical and mean-field insights into charge ordering phenomena and phase transitions in the extended Hubbard model on the Bethe lattice.

Findings

Increasing onsite repulsion suppresses charge order.

Finite-temperature phase diagrams show transitions between insulating and metallic states.

Analytical results avoid numerical inaccuracies of other methods.

Abstract

We study the extended Hubbard model (EHM) with both onsite Hubbard interaction and the intersite density-density interaction between nearest-neighbors using the standard Hartree mean-field approximation (MFA) on the Bethe lattice. We found that, at the ground state, the system can be in a charge-ordered insulating (COI), a charge-order metallic (COM) or a non-charge-ordered (NO) state. Moreover, the finite-temperature phase diagrams are presented. Several observables like a charge-order parameter, a spectral function, and particularly at finite temperatures, a charge carrier concentration (to visualize the degree of metallicity) are analyzed. The results show that increasing onsite repulsion suppresses charge order and change the properties of the system from insulating to metallic. Worth noting, that a number of phenomena can be found within the MFA, where their analysis is much simpler than in more advanced approaches. The method used for the EHM on the Bethe lattice also allows for a series of analytical derivations and simplification to see general geometry-independent features and analytical results, avoiding the numerical inaccuracies and other issues that appear with a purely numerical solution.