Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid

TL;DR

This review introduces the Hatsugai-Kohmoto model, an exactly solvable strongly correlated electron system, highlighting its non-Fermi liquid behavior, thermodynamics, and correlation functions, with recent developments since 2020.

Contribution

It provides a comprehensive pedagogic overview of the HK model's properties, including emergent non-Fermi liquid behavior and perturbation analysis, filling a gap in accessible literature.

Findings

HK model exhibits non-Fermi liquid behavior

Thermodynamics and correlation functions are characterized

Perturbation theory and renormalization group analyses are applied

Abstract

This pedagogic review aims to give a gentle introduction to an exactly solvable model, the Hatsugai-Kohmoto (HK) model, which has infinite-ranged interaction but conserves the center of mass. Although this model is invented in 1992, intensive studies on its properties ranging from unconventional superconductivity, topological ordered states to non-Fermi liquid behaviors are made since 2020. We focus on its emergent non-Fermi liquid behavior and provide discussion on its thermodynamics, single-particle and two-particle correlation functions. Perturbation around solvable limit has also been explored with the help of perturbation theory, renormalization group and exact diagonalization calculation. We hope the present review will be helpful for graduate students or researchers interested in HK-like models or more generic strongly correlated electron systems.