Two-orbital Hubbard model vs spin $S=1$ Heisenberg model: studies on clusters

TL;DR

This study compares the two-orbital Hubbard model and the spin S=1 Heisenberg model on a four-site cluster, analyzing their energy spectra and thermodynamic properties to determine the conditions under which they are equivalent.

Contribution

It provides a detailed numerical comparison between the two models, identifying the parameter range where the Heisenberg model accurately approximates the Hubbard model and exploring effects of interorbital hoppings.

Findings

Heisenberg model reproduces Hubbard model spectra within specific interaction parameters.

Interorbital hoppings significantly modify the energy spectrum outside the ideal range.

Modifications influence the temperature dependence of the specific heat.

Abstract

We perform exact numeric calculations for the two-orbital Hubbard model on the four-site cluster. In the limit of large on-site coupling the model becomes equivalent to the spin $S=1$ Heisenberg model. By comparing energy spectra of these two models, we quantified the range of interaction parameters for which the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model. Then we examined how the spectrum evolves when we are outside of this region, focusing especially on checking of how it is modified when various ways of interatomic hoppings of electrons between different orbitals are taken into account. We finally show how these modifications affect the dependence of specific heat on temperature.