Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

Abstract

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N -> \infty, these collective excitations form a continuum in (q,ω)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor S_{zz}(q,ω) are calculated directly from the Bethe wave functions for finite N. The resulting lineshape predictions for N -> \infty complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of S_{zz}(q,ω) in the zero-field limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.