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• W1560322521 abstract "We study the ground-state (gs) phases of the spin-half anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is a frustrated antiferromagnetic (AFM) $J_{1}$--$J_{2}$ system on the checkerboard lattice, with nearest-neighbor exchange bonds $J_{1}>0$ and next-nearest-neighbor bonds $J_{2} equiv kappa J_{1} > 0$. Using various AFM classical ground states as CCM model states we present results for their gs energy, average on-site magnetization, and susceptibilities to plaquette valence-bond crystal (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the state with Neel ordering is the gs phase for $kappa < kappa_{c_1} approx 0.80 pm 0.01$, but that none of the fourfold set of AFM states selected by quantum fluctuations at $O(1/s)$ in a large-$s$ analysis (where $s$ is the spin quantum number) from the infinitely degenerate set of AFM states that form the gs phase for the classical version of the model (for $kappa>1$) survives the quantum fluctuations to form a stable magnetically-ordered gs phase for the spin-half case. The Neel state becomes susceptible to PVBC ordering at or very near to $kappa = kappa_{c_1}$, and the fourfold AFM states become infinitely susceptible to PVBC ordering at $kappa = kappa_{c_2} approx 1.22 pm 0.02$. In turn, we find that these states become infinitely susceptible to CDVBC ordering for all values of $kappa$ above a certain critical value at or very near to $kappa = kappa_{c_2}$. We thus find a Neel-ordered gs phase for $kappa<kappa_{c_1}$, a PVBC-ordered phase for $kappa_{c_1} < kappa < kappa_{c_2}$, and a CDVBC-ordered phase for $kappa > kappa_{c_2}$. Both transitions are probably direct ones, although we cannot exclude very narrow coexistence regions confined to $0.79 lesssim kappa lesssim 0.81$ and $1.20 lesssim kappa lesssim 1.22$ respectively." @default.
• W1560322521 created "2016-06-24" @default.
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• W1560322521 date "2012-05-11" @default.
• W1560322521 modified "2023-09-30" @default.
• W1560322521 title "Frustrated Heisenberg antiferromagnet on the checkerboard lattice:<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>-<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>model" @default.
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• W1560322521 doi "https://doi.org/10.1103/physrevb.85.205122" @default.
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