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

TL;DR

This paper introduces an exactly solvable two-orbital model with infinite-range interactions, revealing novel quantum phases and phase transitions that could shed light on complex electron behaviors in correlated materials.

Contribution

The paper presents a new solvable periodic Anderson model with infinite-range interactions, enabling analysis of quantum states and phase transitions across different dimensions.

Findings

Discovery of non-Fermi-liquid-like metallic states violating Luttinger theorem

Identification of hybridization-driven insulators and Mott insulators

Observation of Lifshitz transition universality in quantum phase changes

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$_{12}$.