Quantum spin chains in a magnetic field

We demonstrate that the “worm” algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its autocorrelation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2\mathrm{}$ and $s=1\mathrm{}$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green-function analysis we deduce the magnon spectra in the $s=1\mathrm{}$ system, and directly establish the “relativistic” form $E\left(p\right)=({\Delta }^2{+v}^2{p}^2{)}^{1/2}$ of the dispersion law.