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

TL;DR

This work investigates quantum effects on the magnon spectrum of a 2D spin-1/2 altermagnetic Heisenberg model on a square lattice using momentum-space continuous similarity transformations to obtain a magnon-number-conserving effective Hamiltonian. By applying two CST generators and a scaling-dimension-based truncation, the authors quantify the one-magnon dispersion, magnon-magnon interactions, and dynamical structure factors, while mapping Néel-phase stability via flow convergence. They report that magnon interactions reduce the altermagnetic spin splitting by about 14–20% relative to linear spin-wave theory and induce a finite roton depth that grows with positive next-nearest-neighbor coupling J2, signaling enhanced quantum fluctuations. Spectral densities reveal weight transfer from single-magnon to multi-magnon continua, with a stronger three-magnon continuum for J2>0 and roton features consistent with nonclassical magnon dynamics, providing a framework for interpreting future experiments on altermagnets.

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 Néel-ordered phase or the presence of significant magnon decay.

Figures (10)

• Figure 1: (a) Sketch of the spin model \ref{['eq::altermagnet']} on the square lattice split into the two sublattices A and B, lattice vectors $\symbf{a} _1$ and $\symbf{a} _2$ of the magnetic unit cell, antiferromagnetic coupling $J_1$, and the couplings $J_2^{\newline}$ and $J_2^\prime$. (b) Magnon bands $\omega^\downarrow$ and $\omega^\uparrow$ obtained from in the Néel phase for $J_2^{\newline} = -0.2J_1$, and $J_2^\prime=0$. The lattice constant is set to unity.
• Figure 2: Linear extrapolation of the different endpoints of convergence for the analyzed parameter regime with $J_2'=0$. The convergence endpoints for both the $0n$ and the generator are shown depending on the inverse linear system size $1/L$. For $0n$, only an upper set of endpoints is found.
• Figure 3: Dispersions of the $\omega^\downarrow$ and $\omega^\uparrow$ magnon mode obtained from (dashed lines), (dotted lines) and ($L=16$; crosses) along a high-symmetry path for (a) $J_2 = -0.16$, (b) $J_2 = 0$, and (c) $J_2 = +0.16$ for $J_2^\prime = 0$.
• Figure 4: The upper panel depicts the altermagnetic spin splitting $\Delta S$ for different $J_2$, where $J_2<0$ ($J_2>0$) corresponds to ferromagnetic (antiferromagnetic) coupling. The lower panel shows the spin splitting in and relative to .
• Figure 5: The upper panel shows the dispersion $\omega^\downarrow(k)$ for the two point $k=\left(\pi/2,\pi/2\right)$ (circles) and $k=\left(\pi,0\right)$ (triangles). The lower panel shows the resulting roton minimum $\Delta R$ for different $J_2$, where $J_2<0$ ($J_2>0$) corresponds to ferromagnetic (antiferromagnetic) next-nearest neighbor coupling. Results are shown for both and .