Haldane phase in one-dimensional topological Kondo insulators

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.

Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

“…Theoretical studies of the low-temperature resistivity plateau in SmB 6 has brought rich, new physics in describing how strong spin-orbit coupling can give rise to nontrivial topological phases with exotic physical manifestations such as robust metallic surface states [1][2][3]. In these studies, the threedimensional SmB 6 was modeled as a Kondo insulator with spin-orbit coupling that hybridized conduction and f electrons.…”

“…In these studies, the threedimensional SmB 6 was modeled as a Kondo insulator with spin-orbit coupling that hybridized conduction and f electrons. Known as the topological Kondo insulator (TKI), the main factor that contributes to the nontrivial topological property of this model is the odd parity of the f -electron orbital structure that respects spatial-inversion and time-reversal symmetry [1].…”

Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly interacting to the noninteracting limit

“…More importantly, the results in Ref. [33][34][35][36][37] put in evidence the risk of using mean-field approaches to interpret the properties of strongly-interacting topological phases.…”

“…Analyzing the symmetries of this model in the mean-field approximation, these authors argued that it should be classified as a class-D insulator, according to the free-fermion topological classes [6][7][8]. Soon after, using Abelian bosonization, density matrix renormalization group (DMRG), and quantum Monte Carlo techniques, the ground state of 1DTKIs was identified as a Haldane-type insulating phase [33][34][35][36][37], which has no evident connection to the non-interacting topological classes of Refs. [6][7][8].…”

“…This model is closely related to the (interacting) Shockely-Tamm [45,46] or Creutz-Hubbard ladder [47,48] models, and is such that when U = 0 it describes a time-reversal invariant Z 2 -topological band-insulator [1,37], and when U t s , t sp it can be mapped via a canonical transformation onto the 1D p−wave KondoHeisenberg model, with Kondo and Heisenberg exchange couplings J K = 8t 2 sp /U and J K = 4t 2 s /U , respectively, and where the ground state is a SPT phase of the Haldane type [34]. In what follows, t s will be the unit of energies.…”