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arXiv:cond-mat/9511034 · Physical Review Letters

Plaquette Resonating-Valence-Bond Ground State of Ca V4 O9

Kazuo Ueda, Hiroshi Kontani, Manfred Sigrist, Patrick A. Lee

Published Mar 11, 1996• 121 citations
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Abstract

A theoretical model is presented to explain the spin gap observed for $\mathrm{CaV}{}_{4}\mathrm{O}{}_{9}$. The underlying lattice of the 1/5-depleted square lattice favors a formation of the plaquette resonating-valence-bond state. Inclusion of the frustrating second neighbor interaction enhances this tendency, leading to a quantum disordered state of a two-dimensional spin-1/2 Heisenberg model with a sufficiently big spin gap compatible with experiments.

DOI
10.1103/physrevlett.76.1932

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A theoretical model is presented to explain the spin gap observed for CaV4O9\mathrm{CaV}{}_{4}\mathrm{O}{}_{9}CaV4​O9​. The underlying lattice of the 1/5-depleted square lattice favors a formation of the plaquette resonating-valence-bond state. Inclusion of the frustrating second neighbor interaction enhances this tendency, leading to a quantum disordered state of a two-dimensional spin-1/2 Heisenberg model with a sufficiently big spin gap compatible with experiments.
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Using both exact diagonalizations and diagonalizations in a subset of short-range valence-bond singlets, we address the nature of the groundstate of the Heisenberg spin-1∕21∕21∕2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)∕J1=1∕2({J}_{2}+{J}_{3})∕{J}_{1}=1∕2(J2​+J3​)∕J1​=1∕2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore, a careful analysis of dimer-dimer correlation functions, dimer structure factors and plaquette-plaquette correlation functions provides striking evidence for the presence of a plaquette valence bond crystal order in part of the magnetically disordered region.
We examine the ground state and the excitations of an one-dimensional Heisenberg spin 1/2 antiferromagnet with alternating dimers and four-spin plaquettes (dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exact-numerical and perturbational results are presented. We find that the system is gapped for all parameter values. For the latter one we find an effective S=1 Haldane like behaviour in the limit of dominating dimer bonds. The model considered is related to the recently found 1/5-depleted square-lattice Heisenberg system CaV4O9CaV_4O_9CaV4​O9​.
We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor J1{J}_{1}J1​ and second-neighbor J2{J}_{2}J2​ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at J2/J1<0.50{J}_{2}/{J}_{1}<0.50J2​/J1​<0.50 and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.
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