Long-range interactions in the compressible Heisenberg chain

We investigate the effects of long-range Kac-Baker-type interactions between the ions on the nonlinear coupled magnetic and elastic excitations of the compressible Heisenberg chain. We found analytical expressions for the dynamics of the low-temperature–long-wavelength nonlinear excitations of the elastic and magnetic modes. The dependence on the long-range interaction parameter r shows the existence of low-energy excitations near an upper limit r=$r_c$. Finally, we performed a particle analogy by associating a property of mass to the elastic pulse: the existence of coupled solitons is found to be related to the finiteness of an effective mass.