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

TL;DR

This paper introduces a generalized Hatsugai-Kohmoto multi-orbital model, exploring its phase diagram and uncovering unconventional magnetic orders, including ferromagnetism and bond-centered p- and d-wave magnets, with exact solutions revealing rich spectral properties.

Contribution

The authors develop a solvable multi-orbital model that exhibits unconventional magnetic phases and analyze how perturbations influence its ground state and symmetry-breaking behaviors.

Findings

Unconventional ferromagnetic, p-wave, and d-wave magnetic orders are stabilized.

Adding specific interactions yields a non-degenerate singlet ground state with spin splitting.

The model's spectral functions show regimes similar to unconventional magnets.

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.