Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations

TL;DR

This paper uses continuous similarity transformations to analyze quantum effects on magnon excitations in 2D altermagnets, revealing band splitting, roton minima, and phase breakdowns.

Contribution

It introduces a novel application of continuous similarity transformations to study magnon spectra in 2D altermagnets, providing detailed insights into quantum effects and phase stability.

Findings

Magnon dispersion and interactions are quantitatively calculated.

Altermagnetic spin splitting of magnon bands is characterized.

Divergencies indicate phase breakdowns or magnon decay regions.

Abstract

We investigate quantum effects on magnon excitations in a minimal spin-1/2 Heisenberg model for 2D altermagnets on the square lattice. A continuous similarity transformation is applied in momentum space to derive an effective Hamiltonian that conserves the number of magnon excitations. This allows us to quantitatively calculate the one-magnon dispersion, the effects of magnon-magnon interactions, and the dynamic structure factor in a certain range of parameters. In particular, we focus on the altermagnetic spin splitting of the magnon bands and the size of the roton minimum. We further map out divergencies of the continuous similarity transformation for different types of generators, which signal either the breakdown of the N\'eel-ordered phase or the presence of significant magnon decay.