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 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.Comment: 13 pages, 2 figures, 1 appendix. New version with typos correcte

Haldane phase in one-dimensional topological Kondo insulators

We investigate the groundstate properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the $p$-wave Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization Group method. The non-standard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the "$p$-wave" spin density of conduction electrons, inducing a topologically non-trivial insulating groundstate. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin profile in the groundstate, we show that, at half-filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end-states. Beyond its intrinsic interest as a useful "toy-model" to understand the effects of strong correlations on topological insulators, we show that the $p$-wave Kondo-Heisenberg model can be implemented in $p-$band optical lattices loaded with ultra-cold Fermi gases.Comment: 8 pages, 4 figures, 1 appendi