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arXiv:2604.18684

Hatsugai-Kohmoto-like Models for Altermagnets and Odd-Parity Magnets

Konstantin Rickelt, Denis Sedov, Mathias S. Scheurer

Published Apr 20, 2026• 0 citations
arXivHTMLPDF

Abstract

We introduce a generalized Hatsugai-Kohmoto multi-orbital model and study its phase diagram and physical properties in the additional presence of perturbations that lift any extensive ground-state degeneracies. The unperturbed, exactly solvable model already displays a rich set of spectral functions, including regimes reminiscent of unconventional magnets. We map the first-order study of additional spatially local multi-orbital Hubbard interactions to a Heisenberg model in momentum space, which leads to symmetry-breaking instabilities already at weak coupling. Interestingly, translational-symmetry breaking orders, such as antiferromagnetism, are excluded. Instead, in addition to ferromagnetism, unconventional $p$-wave and $d$-wave magnets occur, characterized by spin order on the bonds of the underlying square lattice. Adding another type of momentum-space interaction, which still allows to solve the model exactly, is shown to stabilize a non-degenerate singlet ground state that retains the spin splitting characteristic of unconventional magnets. We discuss its impact on the spin structure factor. Taken together, our findings show that Hatsugai-Kohmoto-like models provide a rich playground for unconventional magnetism.

DOI
10.48550/arxiv.2604.18684

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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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Recently, a quantum anomalous Hall state at odd-integer filling in moir\'e stacked MoTe2/WSe2{\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}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 fff or ddd 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 fff or ddd 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.