Two-magnon states in the one-dimensional isotropic heisenberg model with free boundary conditions

The eigenfunctions and eigenvalues of the energy of two-magnon states in the finite one-dimensional isotropic Heisenberg model S = 1/2 with free boundary conditions were found by solving the Schrödinger equation. The obtained solutions are single-parametric in contrast to two-parametric solutions in the model with cyclic boundary conditions. The amplitudes of the wave functions of coupled two-magnon states exponentially depend on both the distance between the flipped spins and the coordinate of the center of the complex. This leads to a localization of low energy complexes at the ends of the ferromagnetic chain.