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arXiv:1706.02140 · Journal of Superconductivity and Novel Magnetism

Topological Phases Emerging from Spin-Orbital Physics

Wojciech Brzezicki, Mario Cuoco, Filomena Forte, Andrzej M. Oleś

Published Nov 20, 2017• 10 citations
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Abstract

We study the evolution of spin-orbital correlations in an inhomogeneous quantum system with an impurity replacing a doublon by a holon orbital degree of freedom. Spin-orbital entanglement is large when spin correlations are antiferromagnetic, while for a ferromagnetic host we obtain a chain with only orbital interactions. In this regime, the orbital model can be mapped on spinless fermions and we uncover topological phases with zero energy modes at the edge or at the domain between magnetically inequivalent regions.

DOI
10.1007/s10948-017-4416-7

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We study the evolution of spin-orbital correlations in an inhomogeneous quantum system with an impurity replacing a doublon by a holon orbital degree of freedom. Spin-orbital entanglement is large when spin correlations are antiferromagnetic, while for a ferromagnetic host we obtain a chain with only orbital interactions. In this regime, the orbital model can be mapped on spinless fermions and we uncover topological phases with zero energy modes at the edge or at the domain between magnetically inequivalent regions.
Abstract One of the most famous quantum systems with topological properties, the spin S=1{{{{{{{\mathcal{S}}}}}}}}=1S=1 S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic S=1/2{{{{{{{\mathcal{S}}}}}}}}=1/2S=1/2 S = 1 / 2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.
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Spin-orbital entanglement in quantum spin-orbital systems is quantified by a specifically reduced von Neumann entropy and is calculated for the ground state of a coupled spin-orbital chain with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry. By analyzing the discontinuity and local extreme of the reduced entropy, we deduce a rich phase diagram describing quantum phase transitions in this system with complex correlations between multiple degrees of freedom.
We present the entanglement properties of the spin-orbital coupling systems with multiple degrees of freedom. After constructing the maximally entangled spin-orbital basis of bipartite, we find that the quantum entanglement length in the noninteracting itinerant Fermion system with spin and orbit is considerably larger than that in the system with only spin. In the SU(2)⊗\otimes⊗SU(2) spin-orbital interacting system, the entanglement, expressed in terms of the spin-orbital correlation functions, clearly manifests the close relationship with the quantum phases in strongly correlated systems; and the entanglement phase diagram of the finite-size systems is in agreement with the magnetic and orbital phase diagram of the infinite systems. The application of the present theory on nucleon systems is suggested.