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 dependent effects for the 1D isotropic Heisenberg ferromagnet. The results are compared 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 via introduction of cut-offs at the integration limits and analytical continuation from the discrete lattice to the continuous medium. It offers a new perspective on the instability of bound states, and reveals the linear behaviour of the amplitude in the critical region and other features of the model 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 constructing reliable approximations valid for more complicated models. It is concluded that the approach can be useful to study mesoscopic spin systems. PACS. 75.50.Xx Molecular magnets – 75.30.Ds Spin waves