Polarons in quantum chains with XY exchange and Dzyaloshinsky-Moriya interaction
Department of Physics, Faculty of Science, University of Buea PO Box 63 Buea, Buea, Cameroon
Corresponding author: a email@example.com
Revised: 29 January 2007
Published online: 22 March 2007
Excitations of the polaron types are investigated in the spin-1/2 quantum chain with XY exchange and Dzyaloshinsky-Moriya interaction, both coupled to acoustic vibrations of the substrate lattice. The study is carried out via Jordan-Wigner transformation with the help of which the spin chain is mapped onto a chain of spinless fermions. From the resulting effective fermion-lattice Hamiltonian, the discrete equations of motion are derived. These equations are solved in the continuum limit for self-trapped states near the bottom of the fermion spectrum interacting with long-wavelength acoustic lattice modes. The associate polaron solution, which has a pulse shape, is shown to propagate bound to the induced lattice kink distortion by translation along the chain at a constant velocity v. The pair can also experience an additional acceleration ϑ0 when the free fermion charge is excited above its groundstate. The polaron binding energy is strongly reduced, depending quadratically on the ratio D/J of the Dzyaloshinsky-Moriya interaction strength D to the isotropic XY exchange interaction J. It is also found that polaron parameters depend only on the XY spin-lattice coupling but not on the Dzyaloshinsky-Moriya contribution.
PACS: 63.20.Ry – Anharmonic lattice modes / 71.38.-k – Polarons and electron-phonon interactions / 75.10.Pq – Spin chain models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007