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Chaos An Interdisciplinary Journal of Nonlinear Science

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

Zacharie Isidore Djoufack, E. Tala-Tebue, Jean Pierre Nguenang, A. Kenfack-Jiotsa

Published Oct 1, 2016• 19 citations
Publisher

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.

DOI
10.1063/1.4965423

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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.
Abstract We have considered and alternating spin- 1 2 /spin-1 chain with nearest-neighbor (NN) (J 1), next-nearest neighbor (NNN) (J 2) antiferromagnetic (AFM) Heisenberg interactions along with z-component of the Dzyaloshinskii–Moriya (DM) (Dz ) interaction. The Hamiltonian has been studied using (a) linear spin-wave theory and (b) density matrix renormalization group. The system had been reported earlier as a classical ferrimagnet only when NN exchange interactions are present. Both the AFM NNN interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J 2 introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J 1 along with Dz introduces a short range order but develops long range order along the XY plane. J 1 along with J 2 induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the D z term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.
We have considered and alternating Heisenberg spin chain with nearest-neighbor (J1J_1J1​), next-nearest neighbor (J2J_2J2​) antiferromagnetic couplings along with z-component of the Dzyaloshinskii-Moriya(DM) (DzD_zDz​) interactions. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J2J_2J2​ introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J1J_1J1​ along with DzD_zDz​ introduces a short range order but develops long range order along the XY plane. J1J_1J1​ along with J2J_2J2​ induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the DzD_zDz​ term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.
Abstract Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- <?CDATA 12\frac{1}{2}21​?> 1 2 particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- <?CDATA 12\frac{1}{2}21​?> 1 2 dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- <?CDATA 12\frac{1}{2}21​?> 1 2 particle from its initial state.
Most of the existing dynamical studies in one dimension on magnetic insulators have considered the simplest spin models with nearest-neighbor interactions. In real systems, however, it is possible that longer range interactions are not entirely negligible. It is expected that the inclusion of next-nearest-neighbor interactions between spins in one-dimensional spin models will introduce a multitude of new frequencies in addition to the ones already present in the dynamics that arises due to nearest-neighbor interactions. We first present an exact solution for the dynamical xx-spin-pair correlations in an Ising chain with both nearest- and next-nearest-neighbor interactions to confirm our expectation. We next show, via an approximate analytical calculation, that the dynamical zz-spin-pair correlations in the next-nearest-neighbor transverse Ising chain when plotted as a function of time is noticeably different with respect to the exactly solvable nearest-neighbor transverse Ising chain at T\ensuremath{\rightarrow}\ensuremath{\infty} when the next-nearest-neighbor interaction is \ensuremath{\gtrsim}1/2 of the magnitude of the nearest-neighbor interaction. The effects could be fairly subtle in the time domain representation and in the spectral function when these additional interactions are weak (i.e., 1/2 of the nearest-neighbor interaction magnitude). The general conclusions reached in this work are expected to be valid for other simple quantum spin models such as the XY and XXZ models in one dimension. \textcopyright{} 1996 The American Physical Society.
Loss of classicality in alternating spin-12\frac{1}{2}21​/spin-111 chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions
We have considered and alternating Heisenberg spin chain with nearest-neighbor (J1J_1J1​), next-nearest neighbor (J2J_2J2​) antiferromagnetic couplings along with z-component of the Dzyaloshinskii-Moriya(DM) (DzD_zDz​) interactions. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J2J_2J2​ introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J1J_1J1​ along with DzD_zDz​ introduces a short range order but develops long range order along the XY plane. J1J_1J1​ along with J2J_2J2​ induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the DzD_zDz​ term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.
The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.