Monte Carlo studies of one-dimensional quantum Heisenberg and XY models

The Suzuki-Trotter transformation has been used to transform N-spin S=1/2 Heisenberg and XY chains into two-dimensional (N×2m) classical Ising models with complicated interactions. A Monte Carlo method using multispin flipping techniques is then used to study these models for kT/|J|≥0.0125 and m≤10. Finite-size scaling is used to analyze the low-temperature susceptibility of the ferromagnetic Heisenberg chain, and we find a power-law divergence χ=T^-γ with γ=1.32±0.13. Difficulties in the method, particularly due to singular bonding, are discussed.