Geometrical frustration of an extended Hubbard diamond chain in the quasi-atomic limit

TL;DR

This paper investigates the geometrical frustration in an extended Hubbard model on a diamond chain, revealing various frustrated and ordered phases, and provides exact solutions for thermodynamic properties using a mapped effective model.

Contribution

It introduces a novel application of decoration transformation to electron systems, mapping the extended Hubbard model onto an effective model with multi-body interactions, and solves it exactly.

Findings

Identification of five frustrated and four non-frustrated phases.

Exact solution of the effective model via transfer matrix method.

Analysis of thermodynamic properties including chemical potential, entropy, and specific heat.

Abstract

We study the geometrical frustration of extended Hubbard model on diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites, while the rest of them represent only the Coulomb repulsion one. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of non-frustrated ones, ordered antiferromagnetically. Although decoration transformation was derived to spin coupling systems, this approach can be applied to electron coupling ones. Thus the extended Hubbard model can be mapped onto another effective extended Hubbard model in atomic limit with additional three and four-body couplings. This effective model is solved exactly through transfer matrix method. In addition, using the exact solution of this model we discuss several thermodynamic properties away from half filled band, such as chemical potential behavior, electronic density, entropy, where we study the geometrical frustration, consequently we investigate the specific heat as well.