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Physica Scripta

Particle-Like Excitations in Many Component Magnon-Phonon Systems

R. Myrzakulov, Oktay K. Pashaev, Kholmirzo T. Kholmurodov

Published Apr 1, 1986• 24 citations

Abstract

It is shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U ( p, q ) isogroup. Two-sublattice XY chain through the Jordan-Wigner transformations reduced to Su-Schriffer-Heeger coupled electron-phonon model in the quasi-one-dimensional conductor polyacetylene (CH) x theory. The Hamiltonian structure of U ( p, q ) Zakharov's system and its "ultrarelativistic" limit (i.e., the Yajima-Oikawa system with U ( p, q ) isogroup) are studied. The linear problem and the generating functionals for infinite series of additional integrals of motion for U ( p , q) Yajima-Oikawa system are constructed. Four types of soliton solutions under different boundary conditions and appropriate integrals of particles number and energy are found. The quasistationary and ultra-relativistic limits are discussed.

DOI: 10.1088/0031-8949/33/4/013

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It is shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U ( p, q ) isogroup. Two-sublattice XY chain through the Jordan-Wigner transformations reduced to Su-Schriffer-Heeger coupled electron-phonon model in the quasi-one-dimensional conductor polyacetylene (CH) x theory. The Hamiltonian structure of U ( p, q ) Zakharov's system and its "ultrarelativistic" limit (i.e., the Yajima-Oikawa system with U ( p, q ) isogroup) are studied. The linear problem and the generating functionals for infinite series of additional integrals of motion for U ( p , q) Yajima-Oikawa system are constructed. Four types of soliton solutions under different boundary conditions and appropriate integrals of particles number and energy are found. The quasistationary and ultra-relativistic limits are discussed.

A generalized many component Heisenberg spin chain with phonon interaction is proposed. Some reductions of the proposed model leading to different real magnetic systems such as many chained magnetic crystals with nontrivial interchain couplings, a mixture of many chained ferro and antiferromagnets, a colour generalized Pierels-Hubbard model, etc., are studied. It has been shown that the dynamics of all the above real models are close to some integrable systems and coincide with them in certain limits. Such integrable systems are the coupled generalised system of Yajima and Oikawa and U(p, q) nonlinear Schrodinger equation, already well studied.

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasiperiodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. We compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. We discuss implications of our results for the behavior of the dynamic structure factor.

The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.

The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.

The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.

The isotropic

XY

model

(s=1/2)

in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of

N

segments with

n

different exchange interactions and magnetic moments, is exactly solved by introducing the integral Gaussian transformation and the generalized Jordan--Wigner transformation, which reduce the problem to the diagonalization of a finite matrix of

n\text{th}

order. The quantum transitions induced by the transverse field are determined by analyzing the induced magnetization of the cell and the equation of state. The phase diagrams for the quantum transitions, in the space generated by the transverse field and the interaction parameters, are presented. As expected, the model presents multiple, first- and second-order quantum transitions induced by the transverse field, and it corresponds to an extension of the models recently considered by the authors. Detailed results are also presented, at

T=0

, for the induced magnetization and isothermal susceptibility ${\ensuremath{\chi}}_{T}^{zz}$ as a function of the transverse field.