Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions

Abstract

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.

Entanglement Dynamics and Quantum Dense Encoding of Heisenberg Spin Chain in Non-Markovian Environment

“…The Heisenberg model describes the nearest-neighbor spin-exchange interaction, and therefore it is a magnetic quantum system [30] .The J 1 -J 2 spin-chain model [31] is a non-trivial generalization of the in the Heisenberg model, which involves the spin interactions of the nearest and lower neighbors [32][33] . Although it is very difficult to accurately solve the J 1 -J 2 spin chains, the model is solvable with some additional terms [34][35][36][37][38].For example: Popkov and Zvyagin propose double and multi-chain quantum spin models that can be computed [39][40][41][42] ; Ikhlef, Jacobsen and Saleur construct the Z 2 staggered vertex model [43,44] using derivatives of the product of two transfer matrices with different spectral parameters;Tavares and Ribeiro discuss the thermodynamic properties of the system using the quantum transfer matrix method [45,46] . The Hamiltonian of the Heisenberg spin chain model discussed here comes from literature [31] and considers only 2 spins, coupling the Heisenberg spin chain to a Bose environment, the total Hamiltonian of quantum systems in interacting picture are (using natural units in ours context, where all physical quantities are dimensionless physics,  =1):…”

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

“…While recently, Bing Tang et al [14] have analytically shown that quantum breathers with a large number of quanta are possible in ferromagnetic chains with on-site easy axis anisotropy. More recently, Djoufack et al [15] have constructed the quantum soliton and theirs properties in 1D Heisenberg spin chains included Dzyaloshinsky-Moriya interaction for a long range interactions.…”

Dark discrete breather modes in monoaxial chiral helimagnet with easy-plane anisotropy

“…Currently, considerable numerical and theoretical progress has been achieved in understanding the nature of DB in Heisenberg spin chains with additional interactions, for instance, onsite anisotropy or next-nearest-neighbor exchange interactions [20][21][22][23][24][25][26] . Recently, formation of discrete breathers has been analyzed for weak ferromagnetic chains where the presence of the Dzyaloshinskii-Moriya (DM) interaction leads to a small canting between the interacting moments 27,28 . The DB solutions have been examined in dynamics of the 1D array of magnetic particles (dots) with the easy-plane anisotropy and interparticle magnetic dipole interaction 29 .…”