We investigate the relation between magnon, magnon bound states, and the classical soliton solutions in the isotropic, the anisotropic-exchange, and the easy-axis ferromagnetic Heisenberg chains. The Dyson-Maleev boson representation is used to study the interaction between magnons, and bound states are investigated in terms of two-spin Green's functions. For easy-axis and anisotropic-exchange magnets, a mapping to the Bose gas with attractive $\ensuremath{\delta}$-function interactions is established, and it yields the eigenvalues of the magnon and the $m$ th bound state in the weak-coupling and continuum limits. The classical limit of the two-spin Green's function reveals that, to leading order in temperature, the bound-state resonance and the associated effects on the two-magnon continuum survives. An important result is a ${T}^{2}$ dependence of the "binding" energy of the bound-state resonance. As a consequence, in a classical description the bound states enter only in order ${T}^{2}$ . Finally, we quantize the soliton solutions according to the Bohr-Sommerfeld and de Broglie rules. This approach is found to be exact for the $s=\frac{1}{2}$ isotropic Heisenberg chain and for sufficiently small wave numbers for all $s$ values. In the anisotropic-exchange and easy-axis models, it agrees with the results obtained from the mapping on the Bose gas, for large quantum numbers and in the easy-axis case for $s\ensuremath{\gg}\frac{1}{2}$ in addition. On this basis, we conclude that the envelope solitons considered here lead to bound-state resonances and associated effects in a classical treatment. Moreover, their semiclassical quantization gives remarkably accurate energy levels.We investigate the relation between magnon, magnon bound states, and the classical soliton solutions in the isotropic, the anisotropic-exchange, and the easy-axis ferromagnetic Heisenberg chains. The Dyson-Maleev boson representation is used to study the interaction between magnons, and bound states are investigated in terms of two-spin Green's functions. For easy-axis and anisotropic-exchange magnets, a mapping to the Bose gas with attractive $\ensuremath{\delta}$-function interactions is established, and it yields the eigenvalues of the magnon and the $m$th bound state in the weak-coupling and continuum limits. The classical limit of the two-spin Green's function reveals that, to leading order in temperature, the bound-state resonance and the associated effects on the two-magnon continuum survives. An important result is a ${T}^{2}$ dependence of the "binding" energy of the bound-state resonance. As a consequence, in a classical description the bound states enter only in order ${T}^{2}$. Finally, we quantize the soliton solutions according to the Bohr-Sommerfeld and de Broglie rules. This approach is found to be exact for the $s=\frac{1}{2}$ isotropic Heisenberg chain and for sufficiently small wave numbers for all $s$ values. In the anisotropic-exchange and easy-axis models, it agrees with the results obtained from the mapping on the Bose gas, for large quantum numbers and in the easy-axis case for $s\ensuremath{\gg}\frac{1}{2}$ in addition. On this basis, we conclude that the envelope solitons considered here lead to bound-state resonances and associated effects in a classical treatment. Moreover, their semiclassical quantization gives remarkably accurate energy levels.

Physical review. B, Condensed matterNov 1, 198162 citations

Solitons and spin complexes in the anisotropic Heisenberg chain

I. G. Gochev

Physics Letters AApr 1, 198211 citations

Two-magnon states in the one-dimensional isotropic heisenberg model with free boundary conditions

Sergey N. Martynov

Theoretical and Mathematical PhysicsNov 1, 19971 citation

Excitation Spectrum of the Ising-Heisenberg Chain Ferromagnet

T. Schneider, E. Stoll

Results are presented and interpreted for the zero- and finite-temperature excitation spectrum of ferromagnetic Ising-Heisenberg chains, as probed by dynamic form factors. Finite-chain calculations demonstrate the occurrence of a thermally induced resonance centered around zero frequency, and a broadening of the magnon and two-magnon bound-state resonances at low $T$ . The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.Results are presented and interpreted for the zero- and finite-temperature excitation spectrum of ferromagnetic Ising-Heisenberg chains, as probed by dynamic form factors. Finite-chain calculations demonstrate the occurrence of a thermally induced resonance centered around zero frequency, and a broadening of the magnon and two-magnon bound-state resonances at low $T$. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.

Physical Review LettersAug 3, 198128 citations

Non-string two-magnon configurations in the isotropic Heisenberg magnet

Artem Vladimirov

Physics Letters ANov 1, 198450 citations

Excitation spectrum of the ferromagnetic Ising-Heisenberg chain at zero field

T. Schneider, E. Stoll

The excitation spectrum of the ferromagnetic $s=\frac{1}{2}$ Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with $s>\frac{1}{2}$ , such as CsNi ${\mathrm{F}}_{3}$ , and on the soliton aspect of the classically treated systems.The excitation spectrum of the ferromagnetic $s=\frac{1}{2}$ Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with $s>\frac{1}{2}$, such as CsNi${\mathrm{F}}_{3}$, and on the soliton aspect of the classically treated systems.

Physical review. B, Condensed matterApr 1, 198226 citations

m

th bound state in the weak-coupling and continuum limits. The classical limit of the two-spin Green's function reveals that, to leading order in temperature, the bound-state resonance and the associated effects on the two-magnon continuum survives. An important result is a

{T}^{2}

dependence of the "binding" energy of the bound-state resonance. As a consequence, in a classical description the bound states enter only in order

{T}^{2}

. Finally, we quantize the soliton solutions according to the Bohr-Sommerfeld and de Broglie rules. This approach is found to be exact for the

s=\frac{1}{2}

isotropic Heisenberg chain and for sufficiently small wave numbers for all

s

values. In the anisotropic-exchange and easy-axis models, it agrees with the results obtained from the mapping on the Bose gas, for large quantum numbers and in the easy-axis case for $s\ensuremath{\gg}\frac{1}{2}$ in addition. On this basis, we conclude that the envelope solitons considered here lead to bound-state resonances and associated effects in a classical treatment. Moreover, their semiclassical quantization gives remarkably accurate energy levels.

T

. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.

The excitation spectrum of the ferromagnetic

s=\frac{1}{2}

Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with

s>\frac{1}{2}

, such as CsNi

{\mathrm{F}}_{3}

, and on the soliton aspect of the classically treated systems.