Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling

Dorota Gotfryd,Krzysztof Wohlfeld,Ekaterina Pärschke,Andrzej M Oleś

doi:10.3390/condmat5030053

Abstract

Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)⊗SU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.

Highlights

Quantum complex matter is characterized by several intertwined degrees of freedom
We have investigated the level of spin-orbital entanglement in the ground state in the presence of finite spin-orbit coupling and identified small and large λ regimes along the special α + β = 0 line in the model (1) [1]
We first complement the analysis of Ref. [1] with the data for the entanglement entropy in the intermediate regime of λ/J, building a global picture of spin-orbital entanglement under increasing λ

Summary

Introduction

Quantum complex matter is characterized by several intertwined degrees of freedom. Mott insulators with orbital degeneracy belong to this class of materials and are typically characterized by entangled spin-orbital states, either only in the excited states or in the ground state as well. We shall present the spin-orbital entanglement in a broader context, summarizing important results that have been accumulated over the years. With this background established, we will focus on the recent study [1] of the evolution of spin-orbital entanglement with increasing Ising spin-orbit coupling, enriching this story with further details. The importance of orbitals, besides spins, in the effective description of such systems was pointed out long ago by Kugel and Khomskii [4] After this pioneering work, it has been realized that orbital operators are quantum in nature, enforcing equal treatment with electron spins and producing joint spin-orbital fluctuations [5], both in the ground [6,7] and in excited [8,9] states. Quantum fluctuations are further amplified by the spin-orbit coupling [10]

Methods

Results

Conclusion