https://doi.org/10.1140/epjb/e2012-20707-1
Regular Article
Quantum breathers in a finite Heisenberg spin chain with antisymmetric interactions
1 Nonlinear Physics and Complex Systems Group, Département de Physique, École Normale Supérieure, Universitéde Yaoundé I, B.P. 47, Yaoundé, Cameroon
2 Materials Sciences Laboratory, Department of Physics, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
3 A.S. International Centre for Theoretical Physics, Strada Costiera 11, Trieste, Italy
4 Fundamental Physics Laboratory. Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of Sciences, University of Douala, P.O. Box 24157, Douala, Cameroon
a
e-mail: nguenang@yahoo.com
Received: 28 August 2011
Received in final form: 5 January 2012
Published online: 14 March 2012
A study of the likelihood of quantum breathers in a quantum Heisenberg spin system including a Dzyaloshinsky-Moriya interaction (DMI) is done through an extended Bose-Hubbard model while using the scheme of few body physics. The energy spectrum of the resulting Bose-Hubbard Hamiltonian, on a periodic one-dimensional lattice containing more than two quanta shows interesting detailed band structures. From a non degenerate, and a degenerate perturbation theory in addition to a numerical diagonalization, a careful investigation of these fine structures is set up. The attention is focussed on the effects of various interactions that are; the DMI, the Heisenberg in-plane (X, Y) as well as the out of plane exchange interaction on the energy spectrum of such a system. The outcome displays a possibility of an energy self-compensation in the system. We also computed the weight function of the eigenstates in direct space and in the space of normal modes. From a perturbation theory it is shown that the interaction between the quanta leads to an algebraic localization of the modified extended states in the normal-mode space of the non-interacting system that are coined quantum q-breathers excitations.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012
