The exactly solvable ``H-K'' family of interacting electron models introduced by Hatsugai and Kohmoto have played an important role in recent studies of the effect of wave function topology on the properties of correlation-driven (``Mott'') insulators. The authors show here that the very features that enable the exact solution lead to pathological transport properties including electrical conduction in the notionally insulating gapped Mott state and to divergent responses to applied magnetic fields. Caution is required in interpreting the results of the exact solutions.
The exactly solvable H-K'' family of interacting electron models introduced by Hatsugai and Kohmoto have played an important role in recent studies of the effect of wave function topology on the properties of correlation-driven (Mott'') insulators. The authors show here that the very features that enable the exact solution lead to pathological transport properties including electrical conduction in the notionally insulating gapped Mott state and to divergent responses to applied magnetic fields. Caution is required in interpreting the results of the exact solutions.
The Hatsugai-Kohmoto interaction model has gained a lot of attention in recent years, due to the fact it is exactly solvable in momentum space in any dimension while capturing some key features of the Mott phase. Here a one-dimensional lattice model with this interaction is approached from the real-space perspective, to explore how breaking the translation invariance of a lattice affects the intuition built by studying the exact solution in k space. The ground state properties of chains with periodic and open boundary conditions are calculated and compared with both the exact solution in momentum space as well as with analogous solutions of the Hubbard model. The results show that introducing hard edges enhances the ferromagnetic correlations and the system undergoes a magnetic transition before reaching the strong coupling limit. Understanding the impact of hard edges is a crucial step toward answering the looming question of the existence of edge states and other topological phenomena in systems with this type of interaction.
Recently, a quantum anomalous Hall state at odd-integer filling in moir\'e stacked MoTe2/WSe2 was convincingly interpreted as a topological Mott insulator state appearing due to strong interactions in band basis [P. Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, Nat. Commun. 14, 5999 (2023)]. In this work, we aim to analyze the formation of a topological Mott insulator due to interactions in orbital basis instead, being more natural for systems where interactions originate from the character of f or d orbitals rather than band flatness. For that reason, we study an odd-integer filled Anderson lattice model incorporating odd-parity hybridization between orbitals with different degrees of correlations introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological Mott insulating state can be realized in a considered model only when weak intra- and interorbital correlations involving dispersive states are taken into account. Interestingly, we find that all topological transitions between trivial and topological Mott insulating phases are not accompanied by a spectral gap closing, consistent with a phenomenon called first-order topological transition. Instead, they are signaled by a kink developed in spectral function at one of the time reversal invariant momenta. We believe that our approach can provide insightful phenomenology of topological Mott insulators in spin-orbit coupled f or d electron systems.
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.
Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model, which can be understood generally as the minimal model that breaks the nonlocal Z2 symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nat. Phys. 16, 1175 (2020); Huang et al., Nat. Phys. (2022)]. In the current paper, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate 1/T1 and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: (1) the free energy exhibits a local minimum at Tp where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition; (2) a tricritical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime; (3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy functional relative to that in BCS; (4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition; (5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting; (6) the heat-capacity jump is nonuniversal and increases with the Mott scale; (7) Mottness destroys the Hebel-Slichter peak in NMR; and (8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature Tp. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.
Topology of the Fermi surface and universality of the metal-metal and metal-insulator transitions: d-dimensional Hatsugai-Kohmoto model as an example
The earlier theory [1] of the quantum phase transitions related to the change of the Fermi Surface Topology (FST) is advanced. For such transitions the Fermi surface as a quantum critical manifold determined by the Lee-Yang zeros, the order parameter P as the d-volume of the Fermi sea, and the special FST universality class were introduced in [1]. The exactly solvable Hatsugai-Kohmoto (HK) d-dimensional (d=1,2,3) model of interacting fermions is analyzed. We explore the relation between the Lee-Yang zeros, the Luttinger and the plateau (Oshikawa) theorems. The validity of the Luttinger theorem in the HK model is confirmed. It is shown that the order parameter P and the FST universality class describe the transitions between metal and band/Mott insulators, as well as the Lifshitz and van Hove gapless-to-gapless transitions. The gapless phases are established to be the Landau Fermi liquids (metals). In addition to the conventional paradigm with a continuous order parameter, we apply the homology theory to analyze the FST transitions. They are critical points of the Morse function. To quantify FST we use the Euler characteristic, which is calculated for each phase of the HK model. We claim that the FST universality class is robust with respect to interactions and other model details, under the condition that the critical points are non-degenerate.
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.