Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Nonlinear dynamics of a quantum ferromagnetic chain: Spin-coherent-state approach

Radha Balakrishnan, A. R. Bishop

Published Nov 1, 1989• 33 citations
Publisher

Abstract

The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.

DOI
10.1103/physrevb.40.9194

Related papers

Nonlinear excitations on a quantum ferromagnetic chain

Radha Balakrishnan, A. R. Bishop

We use a spin-coherent representation to derive the spectrum of nonlinear excitations in a spin-S quantum ferromagnetic Heisenberg chain in the continuum limit. Quantum effects split the semiclassical spectrum into two branches---a lower branch of spin-wave-like, large-width solitary waves with negligible quantum corrections for all S, and an upper branch of particlelike, small-width solitary waves subject to significant quantum corrections for low S. The stability of these excitations is briefly discussed.

Physical Review Letters•Jul 29, 1985•51 citations

Solitary waves in a 1D isotropic Heisenberg ferromagnet

L G de Azevedo, M. A. De Moura, Chiara Delpiano Cordeiro +1 more

The authors present the derivation of a non-linear Schrodinger equation for the quantum isotropic Heisenberg chain using the coherent-states method combined with the Holstein-Primakoff bosons representation of the spin operator. The solution of this equation gives rise to solitary-waves excitations of the system that are similar to those discussed by Tjon and Wright (1977) for the classical Heisenberg chain. A discussion of their results as compared with others in the literature is made.

Journal of Physics C Solid State Physics•Dec 30, 1982•33 citations

Solitons in quantum Heisenberg chain

Marek Cieplak, Łukasz A. Turski

Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.

Journal of Physics C Solid State Physics•Nov 10, 1980•18 citations

Envelope-kink excitations in a quantum anisotropic antiferromagnetic Heisenberg chain

Zhu-Pei Shi, Guoxiang Huang, Ruibao Tao

From the point of view of the quantum lattice liquid, an attempt is made to understand the nonlinear solitonlike excitations in the quantum anisotropic Heisenberg chain with the help of the coherent-state method. It is argued that the modified terms of the nonlinear Schr\"odinger equation are strongly restricted by the relation between the continuum approximation and the semiclassical approximation represented by two smallness parameters \ensuremath{\eta} and \ensuremath{\epsilon}, respectively. When assuming that \ensuremath{\eta} and \ensuremath{\epsilon} are of the same order (\ensuremath{\eta}\ensuremath{\sim}\ensuremath{\epsilon}), after retaining terms of order O(${\mathrm{\ensuremath{\epsilon}}}^{6}$), the equation of motion of the Bose operators satisfies the cubic nonlinear Schr\"odinger equation. Envelope-kink excitations and energy gaps are obtained. Some relevant physical results are also discussed.

Physical review. B, Condensed matter•Apr 1, 1991•3 citations

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

Kazuo Hida

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum $k$ by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small $k$, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.

arXiv:cond-mat/9404017•Journal of the Physical Society of Japan•Jul 15, 1994•28 citations

Nonlinear excitation in anS=1/2 Heisenberg ferromagnetic chain

Zhu-Pei Shi

Nonlinear excitations in an S=1/2 Heisenberg ferromagnetic chain are investigated by using the squeezed fermion coherent states and the Jordan-Wigner fermionic transformation of spin-1/2 operators. The equation of motion for a fermion operator is a modified Schr\"odinger equation. Solitonlike excitations are obtained, and their spectrum has a linear dispersion at low energies.

Physical review. B, Condensed matter•Feb 1, 1992•3 citations
The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.
We use a spin-coherent representation to derive the spectrum of nonlinear excitations in a spin-S quantum ferromagnetic Heisenberg chain in the continuum limit. Quantum effects split the semiclassical spectrum into two branches---a lower branch of spin-wave-like, large-width solitary waves with negligible quantum corrections for all S, and an upper branch of particlelike, small-width solitary waves subject to significant quantum corrections for low S. The stability of these excitations is briefly discussed.
Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.
From the point of view of the quantum lattice liquid, an attempt is made to understand the nonlinear solitonlike excitations in the quantum anisotropic Heisenberg chain with the help of the coherent-state method. It is argued that the modified terms of the nonlinear Schr\"odinger equation are strongly restricted by the relation between the continuum approximation and the semiclassical approximation represented by two smallness parameters \ensuremath{\eta} and \ensuremath{\epsilon}, respectively. When assuming that \ensuremath{\eta} and \ensuremath{\epsilon} are of the same order (\ensuremath{\eta}\ensuremath{\sim}\ensuremath{\epsilon}), after retaining terms of order O(${\mathrm{\ensuremath{\epsilon}}}^{6}$), the equation of motion of the Bose operators satisfies the cubic nonlinear Schr\"odinger equation. Envelope-kink excitations and energy gaps are obtained. Some relevant physical results are also discussed.
The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum kkk by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small kkk, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.