Quantum Fluctuations and Excitations in Antiferromagnetic Quasicrystals

TL;DR

This paper investigates quantum fluctuations and excitation spectra in antiferromagnetic quasicrystals, revealing magnon-like modes, multifractal high-energy states, and unique dynamical properties linked to quasiperiodic structure in a two-dimensional model.

Contribution

It provides the first detailed numerical analysis of quantum excitations in 2D antiferromagnetic quasicrystals using linear spin-wave theory, reproducing prior Monte Carlo results and uncovering new multifractal and dynamical features.

Findings

Magnon-like low-energy excitations observed.

High-energy states exhibit multifractal characteristics.

Dynamical spin structure factor shows self-similar bifurcations.

Abstract

We study the effects of quantum fluctuations and the excitation spectrum for the antiferromagnetic Heisenberg model on a two-dimensional quasicrystal, by numerically solving linear spin-wave theory on finite approximants of the octagonal tiling. Previous quantum Monte Carlo results for the distribution of local staggered magnetic moments and the static spin structure factor are reproduced well within this approximate scheme. Furthermore, the magnetic excitation spectrum consists of magnon-like low-energy modes, as well as dispersionless high-energy states of multifractal nature. The dynamical spin structure factor, accessible to inelastic neutron scattering, exhibits linear-soft modes at low energies, self-similar structures with bifurcations emerging at intermediate energies, and flat bands in high-energy regions. We find that the distribution of local staggered moments stemming from the inhomogeneity of the quasiperiodic structure leads to a characteristic energy spread in the local dynamical spin susceptibility, implying distinct nuclear magnetic resonance spectra, specific for different local environments.