Excitation spectrum of heisenberg spin chains

In the framework of the Heisenberg model of interacting spins we prove the existence of a continuum of zero-activation excitations in the spectrum of alternant spin chains with a non-singular ground state. It is shown that for certain weak restrictions on the spin moment M, the excitations of the lower part of the spectrum with given M are continuous. The results are extended to the case of spin anisotropy, which effectively appears in the spin Hamiltonian method with the use of the Hartree-Fock approximation. For one-dimensional molecular systems described by the Parizer-Papp-Pople (PPP) Hamiltonian, the existence of a continuum of zero-activation excitations is established, provided that the ground state of the system is nondegenerate and nonsingular.Translated from Teoreticheskaya i Éksperimental' naya Khimiya, Vol. 24, No. 2, pp. 204–208, March–April, 1988.The author thanks A. A. Ovchinnikov and V. Ya. Krivnov for discussions of the results of the study.