Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator

Topological Kondo insulators are strongly correlated materials, where itinerant electrons hybridize with localized spins giving rise to a topologically non-trivial band structure. Here we use non-perturbative bosonization and renormalization group techniques to study theoretically a one-dimensional...

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Bibliographic Details
Published in:arXiv.org 2015-06
Main Authors: Lobos, Alejandro M, Dobry, Ariel O, Galitski, Victor
Format: Article
Language:English
Subjects:
Boundary conditions
Chains
Conduction bands
Degrees of freedom
Electron spin
Ferromagnetism
Heisenberg theory
Insulators
Locking
Mean field theory
Order parameters
Statistical models
Topology
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Summary:Topological Kondo insulators are strongly correlated materials, where itinerant electrons hybridize with localized spins giving rise to a topologically non-trivial band structure. Here we use non-perturbative bosonization and renormalization group techniques to study theoretically a one-dimensional topological Kondo insulator. It is described as a Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel - a strongly correlated version of the prototypical Tamm-Shockley model. We derive and solve renormalization group equations at two-loop order in the Kondo parameter, and find that, at half-filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a non-interacting conduction band (Hubbard parameter \(U=0\)). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-\(1\) chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-\(1/2\) end states for chains with open boundary conditions. Our analysis allows to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
ISSN:2331-8422
DOI:10.48550/arxiv.1411.5357