Generalized hole-particle transformations and spin reflection positivity in multi-orbital systems

TL;DR

This paper introduces a method combining symmetry transformations to analyze the ground state properties of multi-orbital electron models, providing rigorous results on spin, orbital, and pairing pseudospins.

Contribution

It develops a novel approach using combined symmetry transformations to characterize ground state symmetries in multi-orbital Hubbard models.

Findings

Rigorous determination of ground state pseudospins at half-filling.

Analysis of the effects of Hund's rule coupling.

Application to models on bipartite lattices.

Abstract

We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital and $\eta$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models which include the Hund's rule coupling.