Understanding one-dimensional topological Kondo insulator: Poor man's non-uniform antiferromagnetic mean-field theory versus quantum Monte Carlo simulation

Abstract

Topological Kondo insulator (TKI) is an essential example of interacting topological insulator, where electron's correlation effect plays a key role. However, most of our understanding on this timely issue comes from numerical simulations, (particularly in one-spatial dimension) which exactly includes correlation effect but is black box for extracting underlying physics. In this work, we use a non-uniform antiferromagnetic mean-field (nAFM) theory to understand the underlying physics in a TKI model, the $1D$ $p-$wave periodic Anderson model ($p$-PAM). Comparing with numerically exact quantum Monte Carlo simulation, we find that nAFM theory is an excellent approximation for ground-state properties when onsite Hubbard interaction is weak. This emphasizes the dominating antiferromagnetic correlation in this system and local antiferromagnetic picture captures the qualitative nature of interacting many-body ground state. Adding extra conduction electron band to $p$-PAM leads to a quantum phase transition from Haldane phase into topological trivial phase. We believe these results may be helpful for understanding novel physics in interacting TKI materials such as SmB$_{6}$ and other related compounds.