Spin waves and local magnetizations on the Penrose tiling

TL;DR

This paper investigates spin wave excitations and local magnetizations in a quasiperiodic Heisenberg antiferromagnet on the Penrose tiling, revealing low-energy extended states, multifractal eigenmodes, and localized high-energy states.

Contribution

It provides the first detailed analysis of spin waves and local magnetizations in a quasiperiodic antiferromagnetic system, introducing a simple analytical model for the ground state properties.

Findings

Linear spin wave dispersion with reduced velocity compared to square lattice

Low-energy eigenstates are extended and multifractal

High-energy states are localized and site-dependent

Abstract

We consider a Heisenberg antiferromagnet on the Penrose tiling, a quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions are studied in the linear spin wave approximation. A linear dispersion law is found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes are characterized in several different ways. At low energies, eigenstates are relatively extended, and show multifractal scaling. At higher energies, states are more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations are calculated. Perpendicular space projections are presented in order to show the underlying simplicity of this "complex" ground state. A simple analytical model, the two-tier Heisenberg star, is presented to explain the staggered magnetization distribution in this antiferromagnetic system.