Quantum Antiferromagnetism in Quasicrystals

TL;DR

This study investigates antiferromagnetic order in a two-dimensional quasiperiodic lattice using quantum Monte Carlo simulations, revealing inhomogeneous magnetic moments and hierarchical structures due to self-similarity, with implications for experimental detection.

Contribution

First detailed quantum Monte Carlo analysis of antiferromagnetism on a quasiperiodic lattice, highlighting inhomogeneity and hierarchical magnetic structures.

Findings

Inhomogeneous distribution of local magnetic moments.

Hierarchical structure arising from lattice self-similarity.

Antiferromagnetic modulations detectable in experiments.

Abstract

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. The distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, using the Stochastic Series Expansion Quantum Monte Carlo method. A non-trivial inhomogeneous ground state is found. For a given local coordination number, the values of the magnetic moments are spread out, reflecting the fact that no two sites in a quasicrystal are identical. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. Furthermore, the computed spin structure factor shows antiferromagnetic modulations that can be measured in neutron scattering and nuclear magnetic resonance experiments. This generic model is a first step towards understanding magnetic quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.