Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J1-J2 model

R. F. Bishop, P. H Y Li, D. J J Farnell, J. Richter, C. E. Campbell

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    Abstract

    We study the zero-temperature ground-state (gs) phase diagram of the spin-1/2 anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is equivalently described as a frustrated J1-J2 antiferromagnet on the two-dimensional checkerboard lattice, with nearest-neighbor exchange bonds of strength J1 > 0 and next-nearest-neighbor bonds of strength J2 ≡ κJ1 > 0. Using various antiferromagnetic
    (AFM) classical ground states as CCM reference states, we present results for the gs energy, average local on-site magnetization, and the susceptibilities of these states against the formation of plaquette valence-bond crystal
    (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the AFM quasiclassical state with N´eel ordering is the gs phase for κ < κc1
    ≈ 0.80 ± 0.01, but that none of the infinitely degenerate set of AFM states that form the gs phase for the classical version (s →∞) of the model (for κ > 1) survive the quantum fluctuations to form a stable magnetically ordered gs phase for the s = 1/2 case. Instead, our calculations indicate a PVBC-ordered phase for κc1 < κ < κc2 ≈ 1.22 ± 0.02, and a CDVBC-ordered phase for all κ > κc2 . Both transitions are likely to be direct ones, although we cannot exclude very narrow coexistence regions confined to 0.79 ≤ κ ≤ 0.81 and 1.20 ≤ κ ≤ 1.22 respectively.
    Original languageEnglish
    Article number205122 (11pp)
    JournalPhysical Review B (Condensed Matter and Materials Physics)
    Volume85
    DOIs
    Publication statusPublished - 2012

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