Exact Ground States in Spin Systems with Orbital Degeneracy

TL;DR

This paper introduces a method to find exact ground states in spin systems with orbital degeneracy, revealing new valence-bond states and magnetic/orbital orderings in various models.

Contribution

It proposes a novel approach for determining exact ground states in complex spin-orbital models with commuting Hamiltonian components.

Findings

Exact ground states identified for spin-1/2 models with two-fold degeneracy

Discovery of new valence-bond ground states in higher spin and degeneracy models

Characterization of magnetic and orbital ordered states under specific parameters

Abstract

We present exact ground states in spin models with orbital generacy in one and higher dimensions. A method to obtain the exact ground states of the models when the Hamiltonians are composed of the products of two commutable operators is proposed. For the case of the spin-1/2 model with two-fold degeneracy some exact ground states are given, such as the Valence-Bond (VB), the magnetically ordered, and the orbitally ordered states under particular parameter regimes. We also find the models with the higher spin and degeneracy which have the new types of VB ground states in the spin and the orbital sectors.