Finite size corrections within the continuum limit for quantum spins: two-magnon bound states in 1D Heisenberg ferromagnet

A continuum medium approach is proposed to describe the finite size depende nt effects for the ID isotropic Heisenberg ferromagnet. The results are com pared to the exact Bethe ansatz solution for the finite chain. The approach is shown to adequately account for the behaviour of the eigenfunctions and eigenenergies. The continuum is obtained by integration in Fourier space v ia introduction of cut-offs at the integration limits and analytical contin uation from the discrete lattice to the continuous medium. It offers a new perspective on the instability of bound states, and reveals the linear beha viour of the amplitude in the critical region and other features of the mod el in an analytical way. We further apply this approach to investigate the long wavelength expansion of the master equation and to show the route of c onstructing reliable approximations valid for more complicated models. It i s concluded that the approach can be useful to study mesoscopic spin system s.