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
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]
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