Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond

Abstract

In this paper we introduce a solvable two-orbital/band model with 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. Case study on a one-dimension ($1D$) chain shows that the ground-states have Luttinger theorem-violating non-Fermi-liquid-like metallic state, hybridization-driven insulator and interaction-driven featureless Mott insulator. The involved quantum phase transition between metallic and insulating states belongs to the universality of Lifshitz transition, i.e. change of topology of Fermi surface or band structure. Further investigation on $2D$ square lattice indicates its similarity with the $1D$ 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 SmB$_{6}$ and YbB$_{12}$.