Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.
We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.
Department of Telecommunication and Network Engineering, Fotso Victor University Institute of Technology Fotso Victor, University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
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Djoufack
Department of Telecommunication and Network Engineering, Fotso Victor University Institute of Technology Fotso Victor, University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
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Tala-Tebue
Fundamental Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, University of Douala, P.O. Box 24157, Douala, Cameroon.
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Nguenang
Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers' Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon.
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Kenfack-Jiotsa