The Spectral Gap for the Ferromagnetic Spin-J XXZ Chain

摘要: We investigate the spectrum above kink ground states of spin J ferromagnetic XXZ chain with Ising anisotropy �. Our main theorem is that there a non-vanishing gap all this model for values J. Using variety methods, we obtain additional information about magnitude gap, its be- havior large �, overall behavior as function ofand dependence on state, scaling and structure low-lying J, existence isolated eigenvalues in excitation spectrum. By combining in- formation obtained by perturbation theory, numerical, asymptotic analysis arrive at number interesting conjectures. The proof theorem, well some numerical results, rely comparison result Solid-on-Solid (SOS) approximation. This SOS itself raises questions combinatorics, believe it will prove useful study interfaces higher dimensions.