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We investigate a one-dimensional S=1 antiferromagnetic Heisenberg modelcoupled to a lattice distortion by a quantum Monte Carlo method. Investigatingthe ground state energy of the static bond-alternating chain, we find that theinstability to a dimerized chain depends on the value of the spin-phononcoupling, unlike the case of S=1/2. The spin state is the dimer state or theuniform Haldane state depending on whether the lattice distorts or not,respectively. At an intermediate value of the spin-phonon coupling, we find thefirst-order transition between the two states. We also find the coexistence ofthe two states.Comment: 7 pages, 12 eps figures embedded in the text; corrected typos,  replaced figure

physical review. b, condensed matter

Spin-Peierls transition of the first order in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>antiferromagnetic Heisenberg chains

Spin-Peierls transition of the first order inS=1antiferromagnetic Heisenberg chains