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We study the origin of spin-gap in recently discovered material CaV$_4$O$_9$.We analyze the spin-$1/2$ Heisenberg model on the $1/5$ depleted square latticewith nearest neighbor (nn) and next nearest neighbor (nnn) interactions, interms of the singlet and triplet states of the 4-spin plaquettes and 2-spindimers. Phase diagram of the model is obtained within a linear``spin-wave"-like approximation, and is shown to agree well with the earlierresults of QMC simulations for nn interactions. We further propose that thespecial lattice structure of CaV$_4$O$_9$ naturally leads to latticedistortions, which enhances the spin-gap via a spin-Peierls mechanism.Comment: 4 pages, RevTex, 2 postscript figures. Latex file and figures have  been uuencode

physical review letters

Origin of Spin Gap in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>CaV</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>9</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>: Effects of Frustration and Lattice Distortions

Origin of Spin Gap inCaV4O9: Effects of Frustration and Lattice Distortions