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

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.

23 pages, 21 figures

References in corpus (6)

• Percolation quantum phase transitions in diluted magnets
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Quantum phase transitions of the diluted O(3) rotor model
• Quantum-criticality and percolation in dimer-diluted 2D antiferromagnets
• Ordering near the percolation threshold in models of 2D interacting bosons with quenched dilution
• Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution

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