Quasiperiodic Heisenberg antiferromagnets in two dimensions

TL;DR

This review summarizes recent research on two-dimensional quasiperiodic antiferromagnets, highlighting their complex magnetic order, ground state properties, and effects of disorder using various theoretical methods.

Contribution

It provides a comprehensive overview of the ground state and magnetic properties of 2D quasiperiodic antiferromagnets, including effects of disorder, based on multiple theoretical approaches.

Findings

Ground states exhibit Ne9el order with complex spatial magnetization.

Theoretical methods reveal detailed excitation energies and structure factors.

Disorder influences magnetic properties significantly.

Abstract

This is a review of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have N\'eel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented. The effects of introducing geometrical disorder on the magnetic properties are discussed.