Frustration and Entanglement in Compass and Spin-Orbital Models

TL;DR

This paper reviews how intrinsic frustration and spin-orbital entanglement influence the properties of compass and spin-orbital models, affecting ground states, excitations, and potential quantum computing applications.

Contribution

It provides a comprehensive review of the effects of frustration and entanglement in various spin-orbital models, including the Kitaev-Heisenberg model, highlighting their impact on magnetic phases and quasiparticle behavior.

Findings

Robust columnar excitations in nanoscopic compass clusters

Entangled states influence ground and excited states in perovskites

Hole propagation varies from coherent to incoherent across phases

Abstract

We review the consequences of intrinsic frustration of the orbital superexchange and of spin-orbital entanglement. While Heisenberg perturbing interactions remove frustration in the compass model, the lowest columnar excitations are robust in the nanoscopic compass clusters and might be used for quantum computations. Entangled spin-orbital states determine the ground states in some cases, while in others concern excited states and lead to measurable consequences, as in the $R$VO$_3$ perovskites. On-site entanglement for strong spin-orbit coupling generates the frustrated Kitaev-Heisenberg model with a rich magnetic phase diagram on the honeycomb lattice. Frustration is here reflected in hole propagation which changes from coherent in an antiferromagnet via hidden quasiparticles in zigzag and stripe phases to entirely incoherent one in the Kitaev spin liquid.