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

the european physical journal. b, condensed matter physics/european physical journal. b, condensed matter and complex systems

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