Monte Carlo Study of Spin-Peierls Transition in Quasi-One-Dimensional Heisenberg Model with Finite-Frequency Phonons

A quasi-one-dimensional spin-1/2 Heisenberg antiferromagnet coupled with optical phonons is numerically studied by the quantum Monte Carlo method. We have implemented the stochastic series expansion method for the spin part of the Hamiltonian and the path-integral quantization method for the phonon part. Keeping the spin-phonon coupling strength unchanged, we have calculated the spin-Peierls transition temperature as a function of the frequency of optical phonons. It is found that the transition temperature decreases as the phonon frequency increases. Above a critical frequency, the spin-Peierls transition does not occur all the way down to zero temperature due to quantum fluctuations. We have determined the universality class of the spin-Peierls transition by the phenomenological finite-size scaling analysis. The transitions at low frequencies belong to the universality class of the two-dimensional Ising model while that at a high frequency is found to be characterized by the tricritical exponents of the two-dimensional spin-1 Blume-Capel model.