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Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
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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.
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Violation of Luttinger's theorem in one-dimensional interacting fermions
In the strongly interacting 1D t-t'-V model near half-filling, the Luttinger integral deviates from the particle density as zeros in ReG(k,0) appear, signaling a non-Luttinger liquid phase.
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