MONTE-CARLO STUDY OF QUANTUM SPIN CHAINS

Results of a numerical experiment on one-dimensional quantum spin chains are reported. The Heisenberg model with a nearest-neighbor interaction is investigated for spins 1/2 less-than-or-equal-to S less-than-or-equal-to 2. The procedure of measurement in the conventional checkerboard world-line algorithm is modified to give lower systematic errors. In addition to spatial-correlation properties, the magnon spectral density is extracted from the magnon Green function via the fast maximum-entropy algorithm. In particular, the existence of the Haldane gap in S = 1 and S = 2 cases is explicitly demonstrated. Hidden antiferromagnetic order peculiar to the Haldane phase is measured for S = 1 as a function of one-site anisotropy. The mapping onto the restricted solid-on-solid model is analyzed. The difference between systems with even and odd integer spins is discussed.