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

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 SmB6 and other related compounds. Graphical abstract