Zhu-Pei Shi

On soliton excitations in a one-dimensional Heisenberg ferromagnet

Soliton excitations in a one-dimensional Heisenberg ferromagnet are studied by means of the Holstein-Primakoff representation. Writing the Hamiltonian and the equation of motion into dimensionless forms, the authors show that the relative ratio of epsilon to eta is important for the determination of the modified terms of the nonlinear Schrodinger equation; epsilon =1/ square root S (S is the spin length) is the small dimensionless parameter used in the semiclassical approximation and eta =a/ lambda 0 (a is the lattice space and lambda 0 is the characteristic wavelength of the excitations) is another small dimensionless parameter used in the long-wave approximation. The soliton solutions are given in three cases ( eta =O( epsilon ), eta =O( epsilon 32/) and eta =O( epsilon 2)) which correspond to the different physical conditions of the system. The results obtained by Pushkarov and Pushkarov (1977), de Azevedo et al. (1982), and Skrinjar et al. (1989) are included in this approach.

SOLITARY WAVES IN A SPIN CHAIN UNDER A SUPER-LONG-WAVE APPROXIMATION

Solitary waves in a spin chain with biquadratic anisotropic exchange interaction are investigated by means of the Holstein-Primakoff bosonic representation of spin operators. It is argued that the modified terms of the nonlinear Schrodinger equation are restricted strongly by the relative ratio of two small parameters η and e used in long wave approximation and semiclassical approximation respectively. When assuming that η and e2 have the same order (η−e2, the so-called “super-long wave approximation”), after retaining terms of the equivalent order O(e8), we find that the motion of Bose operator in the anisotropic case satisfies Schrodinger equation with high-order nonlinear term α|α|4. Its solitary wave solution and relevant physical results are discussed.

Two-Soliton Bound States in a Heisenberg Spin Chain*

An inhomogeneous Heisenberg spin Hamiltonian with single ion anisotropy is used to investigate the nonlinear excitations in ferromagnetic chain. By means of the Holstein-Primakoff transformation and Glaubers coherent–state representation, the equation of motion for anni-hilation operator a(j) is reduced to a nonlinear Schrodinger-like equation in the semiclassical approximation and the long wave approximation. For a homogeneous system, the exact and explicitly single soliton (localized magnon state) and two–magnon bound state solutions are Given by the inverse scattering transform.

Magnetic Phase Transitions in Quantum Ising Model with Annealed Antiferromagnetic Bond Randomness

The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field, and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.

Double-Chain Mean-Field Renormalization Group Approach for the Ising Model*

A double-chain mean-field renormalization group approach for the Ising model is formulated. With the approach, transition temperatures and critical exponents for several numbers of nearest-neighbor chains are obtained.

Soliton Excitations in the Compressible Heisenberg Spin Chain: A General Approach*

A general approach is given for the nonlinear excitations in the compressible Heisenberg ferromagnetic chain in coherent-state representation. It is shown that the relative ratio of to is very important for determining the nonlinear modified terms of the equations of motion. (S is the spin length) and (a is the lattice constant and is the characteristic wavelength of the excitations) are two small dimensionless parameters used in the semiclassical approximation and in the long wavelength approximation, respectively. In the case of , the reduced equations of motion are solved exactly and spin soliton and elastic kink solutions are obtained. The other cases of the relation between and are also discussed and the solitary wave solutions are also given. The result obtained by Ferrer, as a special case, has been included in our approach.

Phase Transitions in a Highly Anisotropic Antiferromagnetic Heisenberg Toda Chain

The behavior of the antiferromagnetic spin 1/2 Heisenberg Toda chain is investigated in a space of interactions which include exchange anisotropy, bond alternation and Toda-like spinlattice coupling by means of coherent-state for spin. We analyse magnetically driven lattice instabilities and find that multiphase structure only occurs under the condition of bond alternation. Three phase diagrams and tricritical points are obtained and some relevant physical properties are discussed.