Quantum antiferromagnetism in quasicrystals

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. Using the stochastic series expansion quantum Monte Carlo method, the distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, and a nontrivial inhomogeneous ground state is found. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. 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.