Haldane phase in one-dimensional topological Kondo insulators

TL;DR

This paper studies a one-dimensional topological Kondo insulator model using DMRG, revealing a Haldane phase with protected edge states, and discusses its potential realization in cold atom systems.

Contribution

It demonstrates that a $p$-wave Kondo-Heisenberg model exhibits a Haldane phase with topologically protected states, expanding understanding of correlations in topological insulators.

Findings

The system is in the Haldane phase at half-filling.

It hosts topologically protected spin-1/2 end-states.

The model can be realized in cold atom optical lattices.

Abstract

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.