Entangled Spin-Orbital Phases in the d$^9$ Model

TL;DR

This paper explores the complex phase diagrams of the spin-orbital $d^9$ Kugel-Khomskii model on bilayer and monolayer square lattices, revealing various valence bond and entangled phases using the Bethe-Peierls-Weiss method.

Contribution

It introduces a detailed analysis of entangled spin-orbital phases in the $d^9$ model for bilayer systems, expanding understanding of quantum phase behavior.

Findings

Identification of valence bond phases with interlayer and planar singlets

Discovery of two entangled spin-orbital (ESO) phases in bilayer systems

Anticipation of similar entangled phases in monolayer systems

Abstract

We investigate the phase diagrams of the spin-orbital $d^9$ Kugel-Khomskii model for a bilayer and a monolayer square lattice using Bethe-Peierls-Weiss method. For a bilayer we obtain valence bond phases with interlayer singlets, with alternating planar singlets, and two entangled spin-orbital (ESO) phases, in addition to the antiferromagnetic and ferromagnetic order. Possibility of such entangled phases in a monolayer is under investigation at present.