Nature of the low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets

TL;DR

This paper investigates the low-energy excitations in two-dimensional site-diluted Heisenberg antiferromagnets, revealing localized magnetic moments and their impact on dynamic properties, with differences observed at the percolation point and in bilayer models.

Contribution

It provides a detailed analysis of excitation origins, localization, and dynamic exponents, highlighting the role of sublattice imbalance and contrasting single-layer and bilayer systems.

Findings

Localized magnetic moments arise from sublattice imbalance.

Dynamic exponent at the percolation point is approximately 3.6.

Bilayer model exhibits a smaller dynamic exponent, indicating different excitation nature.

Abstract

We present several different calculations pertaining to the nature of the low-energy excitations of the site-diluted S=1/2 Heisenberg antiferromagnet, in particular at the percolation point. We present a picture of excitations originating from an effective low-energy subsystem consisting of localized magnetic moments. At the percolation point, these moments lead to an anomalously large dynamic exponent; z=3.6(1). The magnetic moments are shown to originate from local sublattice imbalance, which we study quantitatively using a classical dimer-monomer model. The localization properties of triplet excitations of clusters with singlet ground state are examined using simulations in the valence bond basis. The triplet is shown to affect predominantly sites on the classical monomer regions. The number of sites affected grows as a non-trivial power of the cluster size. We also study a bilayer model, where there is no sublattice imbalance. Accordingly, we find a much smaller dynamic exponent, consistent with quantum rotor (or possibly fracton) excitations.