Magnon–phonon interaction in the one dimensional quantum XY model

Antonio S. T. Pires

Antonio S. T. Pires

I. G. Gochev

R. Myrzakulov, Oktay K. Pashaev, Kholmirzo T. Kholmurodov

It is shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U ( p, q ) isogroup. Two-sublattice XY chain through the Jordan-Wigner transformations reduced to Su-Schriffer-Heeger coupled electron-phonon model in the quasi-one-dimensional conductor polyacetylene (CH) x theory. The Hamiltonian structure of U ( p, q ) Zakharov's system and its "ultrarelativistic" limit (i.e., the Yajima-Oikawa system with U ( p, q ) isogroup) are studied. The linear problem and the generating functionals for infinite series of additional integrals of motion for U ( p , q) Yajima-Oikawa system are constructed. Four types of soliton solutions under different boundary conditions and appropriate integrals of particles number and energy are found. The quasistationary and ultra-relativistic limits are discussed.

L.S. Lima

We present the low-temperature dynamic properties of the quantum one-dimensional Heisenberg antiferromagnet with integer Spin S with spin-phonon interaction, Dzyaloshins-kii-Moriya interaction and taking into account three magnon processes. First, we present the low-temperature dynamic properties of the quantum one-dimensionalHeisenberg antiferromagnet with integer spin S coupled to phonons. The calculation of the relaxation function is performed using the combination of the memory function formalism with the modified spin-wave theory. The procedure includes up to two-magnon and magnon-phonon processes. We show that the magnon-phonon coupling smooths the double-peak structure obtained for the model in the absence of phonons, when the wavevector q moves from q = ¼. After that, we present a calculation of the in-plane dynamical structure factor for the S = 1 one-dimensional antiferromagnet with a Dzyaloshinskii-Moriya interaction using the Schwinger boson mean-field theory. Then, we present the dynamical properties of the Heisenberg antiferromagnet takinginto account three magnon processes. We calculate the correlation function in time using the modified spin-wave theory. The procedure here includes up to two and three-magnon processes. We show that the double peak structure obtained for the model taking into account two-magnon processes is not smoothed when we take account three-magnon processes too

L.S. Lima