Quantum spin chains in a magnetic field

TL;DR

This paper demonstrates the effectiveness of the worm algorithm in quantum Monte Carlo simulations of spin chains in magnetic fields, providing accurate magnetization curves and magnon spectra, and confirming the relativistic dispersion law.

Contribution

It introduces the worm algorithm for efficient QMC simulations of spin systems in magnetic fields and applies it to analyze magnetization and magnon spectra.

Findings

Worm algorithm enables precise QMC simulations with low auto-correlation times.

Magnetization curves match Bethe ansatz and exact diagonalization results.

Magnon spectra follow a relativistic dispersion law.

Abstract

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 auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ 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 system, and directly establish the "relativistic" form E(p)=(\Delta ^2 +v^2 p^2)^{1/2} of the dispersion law.