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

## TL;DR

This study uses DMRG to explore how a one-dimensional topological insulator transitions into a topological Kondo insulator as interactions increase, revealing a continuous Haldane-type topological phase evolution.

## Contribution

It demonstrates that the ground state remains a symmetry-protected topological phase throughout the interaction range, bridging non-interacting and strongly interacting regimes.

## Key findings

- Ground state classified as Haldane-type SPT phase across interaction strengths
- Adiabatic evolution between non-interacting and strongly interacting limits
- System can be realized in optical lattices with ultra-cold fermionic atoms

## Abstract

We study, by means of the density-matrix renormalization group (DMRG) technique, the evolution of the ground state in a one-dimensional topological insulator, from the non-interacting to the strongly-interacting limit, where the system can be mapped onto a topological Kondo-insulator model. We focus on a toy model Hamiltonian (i.e., the interacting "$sp$-ladder" model), which could be experimentally realized in optical lattices with higher orbitals loaded with ultra-cold fermionic atoms. Our goal is to shed light on the emergence of the strongly-interacting ground state and its topological classification as the Hubbard-$U$ interaction parameter of the model is increased. Our numerical results show that the ground state can be generically classified as a symmetry-protected topological phase of the Haldane-type, even in the non-interacting case $U=0$ where the system can be additionally classified as a time-reversal $\mathbb{Z}_{2}$-topological insulator, and evolves adiabatically between the non-interacting and strongly interacting limits.