Dynamics of three magnons for the Dyson hamiltonian in one dimension

Abstract

For a linear chain of N spins with isotropic ferromagnetic exchange (J > 0 ) between nearest neighbours the complete spectrum of the Dyson hamiltonian is determined within the subspaces of boson occupation number n = 2 and n = 3. In addition to the three-magnon bound state at , there are also present three bound states which do not have their analogue in the Heisenberg chain. One of these states occurs at a real energy E1 = (7/8) J, while the other two are at complex-conjugate energies E2 = (2.06 + 0.496i) J and E3 = E*2.

Using the calculated wave functions, the off-shell three-body T matrix is determined near the bound-state energies. It is found that this T matrix has a very simple analytic structure and it is explicitly verified that it is a solution of the Faddeev equation. Finally, the corresponding equations for the anisotropic case (Jx = Jy = σJ, Jz = J) are briefly discussed.