Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

Alejandro M Lobos,Ariel O Dobry,Victor Galitski

doi:10.1103/physrevx.5.021017

Abstract

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.

Highlights

Starting with the pioneering works of Kane and Mele [1,2] and others [3,4,5], there has been a surge of interest in topological characterization of insulating states [6,7,8]
Our analysis allows us 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
We study theoretically a model for a topological 1D Kondo insulator using the Abelian bosonization formalism and derive the two-loop RG flow equations for the system at half filling

Summary

INTRODUCTION

Starting with the pioneering works of Kane and Mele [1,2] and others [3,4,5], there has been a surge of interest in topological characterization of insulating states [6,7,8]. In the absence of interactions in the fermionic chain (i.e., U 1⁄4 0) and in the large-N mean-field approximation, Alexandrov and Coleman have shown the emergence of topologically protected edge states arising from the nontrivial form of the Kondo term [Eq (3)] [26]. In their mean-field approach, the effective description of the system corresponds to noninteracting quasiparticles filling a strongly renormalized valence band with a nontrivial topology, stemming from the charge conjugation, time reversal, and charge U(1) symmetry of the effectively noninteracting Hamiltonian We substantiate these ideas by providing a rigorous analysis

RENORMALIZATION-GROUP ANALYSIS

CONCLUSIONS

Cγαβ γ