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Physical review. B./Physical review. B

Emergence of a diverse array of phases in an exactly solvable model

Zhipeng Sun, Hai-Qing Lin

Published Mar 5, 2024• 5 citations
Publisher

Abstract

Numerical solvers for strongly correlated electronic systems poses a significant challenge in condensed matter theory. In recent years, extensive exploration of strongly correlated effects has been carried out based on exactly solvable Hatsugai-Kohmoto-like models. In this work, we investigate a simple two-site cluster extension of the Hatsugai-Kohmoto model. The model exhibits a rich variety of phases, including the charge-$4e$ phase, charge-$2e$ phase, metallic phase, pseudogap phase, and Luttinger liquid phase. These findings contribute to the understanding of strongly correlated physics and superconducting physics.

DOI
10.1103/physrevb.109.115108

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Numerical solvers for strongly correlated electronic systems poses a significant challenge in condensed matter theory. In recent years, extensive exploration of strongly correlated effects has been carried out based on exactly solvable Hatsugai-Kohmoto-like models. In this work, we investigate a simple two-site cluster extension of the Hatsugai-Kohmoto model. The model exhibits a rich variety of phases, including the charge-4e4e4e phase, charge-2e2e2e phase, metallic phase, pseudogap phase, and Luttinger liquid phase. These findings contribute to the understanding of strongly correlated physics and superconducting physics.
We propose an exactly solvable lattice model, motivated by the significance of the extended Hubbard model (t−U−Vt-U-Vt−U−V model) and inspired by the work of Hatsugai and Kohmoto. The ground state exhibits a diverse array of phases, including the charge-4e4e4e condensed phase, the charge-2e2e2e superconducting phase, the half-filled insulating phase, the quarter-filled insulating phase, the metallic phase, and an unconventional metallic phase. Among them, the unconventional metallic phase could be of particular significance, for the coexistence of electrons and pairs at zero energy. These findings are poised to advance our understanding and exploration of strongly correlated physics.
We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta k\mathbf{k}k and −k-\mathbf{k}−k. These interactions give rise to novel correlated ground states, leading to a rich phase diagram that includes superconducting, multiple metallic, and Mott-insulating phases. At finite interaction strengths, we observe the emergence of multiple many-body Fermi surfaces, which violate Luttinger's theorem and challenge the conventional Landau-Fermi liquid paradigm. A distinguishing feature of our model is that it remains quantum integrable, even with the addition of pairing interactions of various symmetries, setting it apart from the Hatsugai-Kohmoto model. Our results provide an analytically tractable framework for studying strong correlation effects that give rise to fractionalized excitations and unconventional superconductivity, offering valuable insights into a broad class of integrable many-body systems.
Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity emerging from a half-filled normal state in a two-orbital extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. For a system with point-group symmetry D4h\rm D_{4h}D4h​, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.
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.
Abstract The accurate simulation of strongly correlated electron systems, especially non-Fermi liquid states, remains a central challenge in condensed matter physics, motivating the development of various non-perturbative many-body methods. Such methods are typically benchmarked against determinant quantum Monte Carlo in the Hubbard model, which is limited by the fermionic sign problem and the uncertainties of numerical analytic continuation. To address these issues, we use the exactly solvable Hatsugai–Kohmoto (HK) model as a rigorous testing platform to evaluate three many-body approximations: GW , HGW , and SGW . By comparing Green’s functions, spectral properties, and response functions with exact solutions, we show that the GW approximation, often considered insufficient for describing strong correlation, exhibits a previously unreported solution branch that accurately reproduces the gap structure in the HK model. In addition, using a covariant formalism, we find that HGW provides an accurate description of charge response, while SGW performs well for spin correlations. Our results establish the HK model as a highly effective benchmark system and help refine the understanding of GW methods in strongly correlated regimes.
Abstract Superconductivity in strongly correlated electrons can emerge out from a normal state that is beyond the Landau’s Fermi liquid paradigm, often dubbed as ‘non-Fermi liquid’. While the theory for non-Fermi liquid is still not yet conclusive, a recent study on the exactly-solvable Hatsugai–Kohomoto (HK) model has suggested a non-Fermi liquid ground state whose Green’s function resembles the Yang–Rice–Zhang ansatz for cuprates (2020 Phillips et al Nat. Phys. 16 1175). Similar to the effect of on-site Coulomb repulsion in the Hubbard model, the repulsive interaction in the HK model divides the momentum space into three parts: empty, single-occupied and double-occupied regions, that are separated from each other by two distinct Fermi surfaces. In the presence of an additional Bardeen–Cooper–Schrieffer-type pairing interaction of a moderate strength, we show that the system exhibits a ‘two-stage superconductivity’ feature as temperature decreases: a first-order superconducting transition occurs at a temperature T c that is followed by a sudden increase of the superconducting order parameter at a lower temperature T c ′ < T c . At the first stage, T c ′ < T < T c , the pairing function arises and the entropy is released only in the vicinity of the two Fermi surfaces; while at the second stage, T < T c ′ , the pairing function becomes significant and the entropy is further released in deep (single-occupied) region in the Fermi sea. The phase transitions are analyzed within the Ginzburg–Landau theory. Our work sheds new light on unconventional superconductivity in strongly correlated electrons.