Dynamical spin susceptibility of $d$-wave Hatsugai-Kohmoto altermagnet

TL;DR

This paper studies how electronic correlations affect the spin dynamics in a $d$-wave altermagnetic Hatsugai-Kohmoto model, revealing a Lifshitz transition and a gapped, peaked dynamical susceptibility.

Contribution

It introduces a detailed analysis of the dynamical spin susceptibility in an altermagnetic model with correlations, highlighting a correlation-induced Lifshitz transition and characteristic susceptibility features.

Findings

A many-body Lifshitz transition occurs with increasing interaction.

Dynamical susceptibility develops a gap proportional to interaction strength.

A sharp peak in susceptibility appears and shifts with interaction.

Abstract

We investigate the interplay between altermagnetic band structures and electronic correlations by focusing on the $d_{x^2-y^2}$ altermagnetic generalization of the Hatsugai-Kohmoto model. We find that with increasing interaction, a many-body Lifshitz transition takes place when doubly occupied regions disappear from the Fermi surface and each momentum state becomes fully spin polarized. The spin susceptibility is directly evaluated from the Kubo formula in terms of many-body occupation probabilities. We find that the dynamical susceptibility, which possesses only transverse non-zero components for small wavevectors, develops a gap proportional to the interaction strength, and displays a sharp peak at a frequency increasing with the interaction. %with increasing frequency. Above the Lifshitz transition, this peak moves to the lower gap edge and becomes log-divergent. The signal intensity increases with the interaction up until the Lifshitz transition and saturates afterwards. The static susceptibility remains unaffected by the correlations and altermagnetism reduces the static transverse response.