H. Onishi et S. Miyashita, Spin-Peierls transition of the first order in S=1 antiferromagnetic Heisenberg chains - art. no. 014405, PHYS REV B, 6401(1), 2001, pp. 4405
We investigate a one;dimensional S = 1 antiferromagnetic Heisenberg model c
oupled to a lattice distortion by a quantum Monte Carlo method. Investigati
ng the ground-state energy of the static bond-alternating chain, we find th
at the instability to a dimerized chain depends on the value of the spin-ph
onon coupling, unlike the case of S - 1/2. The spin state is the dimer stat
e or the uniform Haldane state depending on whether the lattice distorts or
not, respectively. At an intermediate value of the spin-phonon coupling, w
e find the first-order transition between the two states. We also find the
coexistence of the two states.