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arXiv:2605.13259

Superconductivity in a Two-Orbital Hatsugai-Kohmoto Model at Half Filling

Nico Hahn, R. Matthias Geilhufe

Published May 13, 2026• 0 citations
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Abstract

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 $\rm D_{4h}$, 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.

DOI
10.48550/arxiv.2605.13259

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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.
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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{\mathbb{Z}}_{2}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/T11/{T}_{1}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{T}_{p}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{T}_{p}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.
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.
We show that the physics of the SU(NNN) Hubbard model can be realistically simulated with the recently developed orbital Hatsugai-Kohmoto model. In this approach, the momentum mixing absent from the band Hatsugai-Kohmoto model is included by grouping nnn-Hubbard atoms into a cluster. We take advantage of the rapid convergence of this scheme (1/n21/n^21/n2) and show that for n≈O(10)n\approx O(10)n≈O(10), quantitative agreement with the determinantal quantum Monte Carlo method arises for the double occupancy as well as qualitative agreement for the filling and compressibility across the Mott transition. Additional features of this work are that we can obtain low-temperature physics, which could be qualitatively different from its high-temperature counterpart, and dynamical quantities without resorting to analytical continuation, thereby establishing the orbital Hatsugai-Kohmoto model as a useful alternative perspective for studying strong correlations in SU(NNN) systems.
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.