Motivated by the non-Fermi liquid (NFL) phase in solvable Hatsugai–Kohmoto (HK) model and ubiquitous quantum oscillation (QO) phenomena observed in strongly correlated electron systems, we have studied the QO in HK model in terms of a combination of analytical and numerical calculation. In the continuum limit, the analytical results indicate the existence of QO in NFL state and its properties can be described by Lifshitz–Kosevich-like formula. Furthermore, numerical calculations with Luttinger’s approximation on magnetic-field-dependent density of state, magnetization and particle’s density agree with the findings of analytical treatment. Although numerical simulation from exact diagonalization exhibits certain oscillation behavior, it is difficult to extract its oscillation period and amplitude. Therefore, more work (especially the large-scale numerical simulation) on this interesting issue is highly desirable and we expect the current HK model study to be helpful in understanding generic QO in correlated electron materials.
Motivated by the non-Fermi liquid (NFL) phase in solvable Hatsugai–Kohmoto (HK) model and ubiquitous quantum oscillation (QO) phenomena observed in strongly correlated electron systems, we have studied the QO in HK model in terms of a combination of analytical and numerical calculation. In the continuum limit, the analytical results indicate the existence of QO in NFL state and its properties can be described by Lifshitz–Kosevich-like formula. Furthermore, numerical calculations with Luttinger’s approximation on magnetic-field-dependent density of state, magnetization and particle’s density agree with the findings of analytical treatment. Although numerical simulation from exact diagonalization exhibits certain oscillation behavior, it is difficult to extract its oscillation period and amplitude. Therefore, more work (especially the large-scale numerical simulation) on this interesting issue is highly desirable and we expect the current HK model study to be helpful in understanding generic QO in correlated electron materials.
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.
When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai-Kohmoto model which has been intensively explored in recent years. Combining T-matrix approximation and linear-response-theory, an interesting picture emerges, if two interaction-induced quasi-particles bands in NFL are partially occupied, FO in this situation is determined by a novel structure in momentum space, i.e. the 'average Fermi surface' (average over two quasi-particle Fermi surface), which highlights the inter-band particle-hole excitation. We hope our study here provides a counterintuitive example in which FO with Fermi surface coexists with NFL quasi-particle, and it may be useful to detect hidden 'average Fermi surface' structure in other 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.
In this study, we investigate the emergence of a topological non-Fermi liquid (NFL) phase in a modified Su-Schrieffer-Heeger (SSH) chain model subjected to long-range interactions characterized by the Hatsugai-Kohmoto (HK) model. While Fermi liquid theory has been instrumental in understanding low-temperature properties of metals, it fails to account for the complex behaviors exhibited by strongly correlated systems, where interactions lead to emergent phenomena such as non-Fermi liquid behavior. Our analysis reveals that the SSH-HK model supports a rich ground state phase diagram, exhibiting distinct NFL phases marked by many-body Zak phases of $2\ensuremath{\pi}$ and 0, corresponding to topological and trivial NFL states, respectively. We demonstrate that the topological NFL state manifests unique electronic polarization characteristics akin to those in the noninteracting SSH model. Through exact diagonalization of the interacting SSH-HK Hamiltonian, we explore the spectral functions and density of states, revealing significant departures from traditional quasiparticle behavior in various particle number sectors. Our findings extend the understanding of topological non-Fermi liquids and their potential implications for high-temperature superconductivity and other correlated electron systems, highlighting the intricate interplay between topology and strong electron correlations.
We study the nonequilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the nonequilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value, or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition and find that its nonanalytic temporal behavior is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for a vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.
The Hatsugai-Kohmoto (HK) model is an exactly solvable electronic lattice model where the interaction between electrons with opposite spin is diagonal in momentum space. We generalize the HK model by introducing momentum-mixing Landau interactions. Within a self-consistent mean-field analysis we find that the ground state of this model exhibits a partially flat energy band, in agreement with the fermion condensation scenario proposed by Khodel and Shaginyan [JETP Lett. 51, 553 (1990)]. Inspired by Andersons pseudospin formulation of BCS theory, we show that the HK model with Landau interactions can be mapped onto a generalized Ising model where each site of the reciprocal lattice hosts two Ising spins. In the pseudospin picture the emergence of a partially flat electronic band corresponds to the smoothing of a magnetic domain wall. Moreover, guided by the pseudospin picture, we propose an exactly solvable variant of the HK model which has a unique ground state for all densities.