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Physical review. B, Condensed matter

Envelope-kink excitations in a quantum anisotropic antiferromagnetic Heisenberg chain

Zhu-Pei Shi, Guoxiang Huang, Ruibao Tao

Published Apr 1, 1991• 3 citations

Abstract

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.

DOI: 10.1103/physrevb.43.8583

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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 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.

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.

Effective nonlinear field theory for a semiclassical long-wavelength description of one-dimensional S=1/2 Heisenberg antiferromagnets with dimerized ground states is derived within an approach using two-site coherent states. The method is applied to bond-alternating anisotropic spin chains in presence of external magnetic field and next-nearest-neighbor interactions. Linear and nonlinear excitations in singlet and magnetic phases are studied. Soliton solutions are found and their properties under semiclassical quantization are discussed. \textcopyright{} 1996 The American Physical Society.

In the recent literature, there have been discussions of nonlinear spin excitations in one-dimensional, anisotropic Heisenberg spin chains. These have the character of localized excitations, which emerge from the time-dependent classical equations of motion. We show that for a given frequency, in a finite spin chain one has a hierarchy of nonlinear excitations, whose envelopes have the appearance of a one soliton, two soliton,..., states. Also, we consider the nature of these nonlinear excitations in an applied magnetic field of frequency \ensuremath{\omega}, and explore aspects of the transient behavior of the system in response to a time varying external field. \textcopyright{} 1996 The American Physical Society.

From the point of view of the quantum lattice liquid, an attempt is made to understand the one-dimensional S =1/2 Heisenberg antiferromagnet. Without assuming a long-range order, the spin wave excitation is approximately derived from the motion of a number operator ( z -component spin). With the aid of a sum rule, the spectrum is estimated. The Boson representation of the system is approximately given on the basis of the equation of motion of the number operator. In this framework, the susceptibility, the specific heat and the correlation function are calculated. The results imply the possibility of a quantum lattice liquid description of the system.