Solvable periodic Anderson model with infinite-range Hatsugai-Kohmoto interaction: Ground-states and beyond
Yin Zhong
Abstract
In this paper we introduce a solvable two-orbital (two-band) model with an infinite-range Hatsugai-Kohmoto interaction, which serves as a modified periodic Anderson model. Its solvability results from strict locality in momentum space and is valid for arbitrary lattice geometry and electron filling. A case study of a one-dimensional chain shows that the ground-states have a Luttinger-theorem-violating non-Fermi-liquid-like metallic state, a hybridization-driven insulator, and an interaction-driven featureless Mott insulator. The involved quantum phase transition between metallic and insulating states belongs to the universality of the Lifshitz transition, i.e., a change of topology of the Fermi surface or band structure. Further investigation on a two-dimensional square lattice indicates its similarity with the one-dimensional case, thus the findings in the latter may be generic for all spatial dimensions. We hope the present model or its modification may be useful for understanding novel quantum states in $f$-electron compounds, particularly the topological Kondo insulator candidates ${\mathrm{SmB}}_{6}$ and ${\mathrm{YbB}}_{12}$.