Topological phase in $1D$ topological Kondo insulator: $Z_{2}$ topological insulator, Haldane-like phase and Kondo breakdown

TL;DR

This study uses quantum Monte Carlo simulations to explore a 1D topological Kondo insulator, revealing a Haldane-like phase with unique edge magnetization properties and emphasizing the importance of interactions in topological states.

Contribution

It demonstrates the existence of a Haldane-like topological phase in a 1D interacting system, highlighting the role of charge fluctuations and the absence of surface Kondo breakdown at zero temperature.

Findings

Identification of Haldane-like state in 1D p-wave Anderson model

Edge magnetization not saturated due to charge fluctuations

No evidence of surface Kondo breakdown at zero temperature

Abstract

We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave Kondo lattice model, though the soluble non-interacting limit corresponds to the conventional $Z_{2}$ topological insulator. The site-resolved magnetization in an open boundary system and strange correlator for the periodic boundary have been used to identify the mentioned topological states. Interestingly, the edge magnetization in the Haldane-like state is not saturated to unit magnetic moment due to the intrinsic charge fluctuation in our periodic Anderson-like model, which is beyond the description of the Kondo lattice-like model in existing literature. The finding here underlies the correlation driven topological state in this prototypical interacting topological state of matter and naive use of non-interacting picture should be taken care. Moreover, no trace of the surface Kondo breakdown at zero temperature is observed and it is suspected that frustration-like interaction may be crucial in inducing such radical destruction of Kondo screening. The findings here may be relevant to our understanding of interacting topological materials like topological Kondo insulator candidate SmB$_{6}$.