On the integrability aspects of the one‐dimensional classical continuum isotropic biquadratic Heisenberg spin chain

1992 ◽  
Vol 33 (5) ◽  
pp. 1807-1816 ◽  
Author(s):  
K. Porsezian ◽  
M. Daniel ◽  
M. Lakshmanan
Keyword(s):  
Spin Chain ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
The One

scholarly journals Symmetry analysis of and first integrals for the continuum Heisenberg spin chain

2002 ◽  
Vol 44 (1) ◽  
pp. 61-72
Author(s):  
M. C. Nucci ◽  
P. G. L. Leach
Keyword(s):  
Differential Equations ◽  
Spin Chain ◽  
Continuum Limit ◽  
Transverse Field ◽  
First Integrals ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
The One ◽  
The Continuum

AbstractDaniel et al. [6] analysed the singularity structure of the continuum limit of the one-dimensional anisotropic Heisenberg spin chain in a transverse field and determined the conditions under which the system is nonintegrable and exhibits chaos. We investigate the governing differential equations for symmetries and find the associated first integrals. Our results complement the results of Daniel et al.

Grain size effect on magnetic and phase transition features in one-dimensional S = 1/2 Heisenberg spin chain molecular crystals

2015 ◽  
Vol 39 (7) ◽  
pp. 5395-5401 ◽  
Author(s):  
Guo-Jun Yuan ◽  
Yun-Xia Sui ◽  
Jian-Lan Liu ◽  
Xiao-Ming Ren
Keyword(s):  
Phase Transition ◽  
Grain Size ◽  
Spin Chain ◽  
Molecular Crystals ◽  
Spin Systems ◽  
Grain Size Effect ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Molecular Spin

Magnetic and thermal behaviors and the phase transition nature are strongly influenced by grain size in one-dimensional S = 1/2 molecular spin systems.

PHOTOEMISSION STUDY OF QUASI-ONE-DIMENSIONAL HALOGEN-BRIDGED COMPOUND [Ni(chxn)2Br]Br2

2002 ◽  
Vol 09 (02) ◽  
pp. 1065-1069
Author(s):  
SHIN-ICHI FUJIMORI ◽  
AKIHIRO INO ◽  
TESTUO OKANE ◽  
ATSUSHI FUJIMORI ◽  
KOZO OKADA ◽  
...  
Keyword(s):  
Brillouin Zone ◽  
Spin Chain ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Energy Dispersion ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Photoemission Study

We report results of the angle-resolved photoemission experiments on a quasi-one-dimensional halogen-bridged complex [Ni(chxn) 2 Br]Br 2 ( chxn = 1R, 2R-cyclohexanediamine), which is a one-dimensional Heisenberg spin chain with S = 1/2 and J ~ 3600 K . The expected two dispersions, originated with spin–charge separations as have been observed in other quasi-one-dimensional electron systems like Sr 2 CuO 3, are not clearly observed in this compound. Instead, only one 'band" having about 0.5 eV energy dispersion is found in the half of the Brillouin zone.

scholarly journals Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap

2015 ◽  
Vol 115 (21) ◽  
Author(s):  
S. Murmann ◽  
F. Deuretzbacher ◽  
G. Zürn ◽  
J. Bjerlin ◽  
S. M. Reimann ◽  
...  
Keyword(s):  
Spin Chain ◽  
Cold Atoms ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain

Quantum breathers in XXZ ferromagnetic chains with on-site easy-plane anisotropy

2016 ◽  
Vol 30 (17) ◽  
pp. 1650100 ◽  
Author(s):  
Bing Tang ◽  
De-Jun Li
Keyword(s):  
Magnetic Moment ◽  
Spin Chain ◽  
Easy Plane ◽  
Hartree Approximation ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Plane Anisotropy ◽  
Existence Conditions ◽  
Quantum Breathers

The existence and properties of quantum breathers in a one-dimensional XXZ ferromagnetic Heisenberg spin chain with single-ion easy-plane anisotropy are investigated analytically in the Hartree approximation. We show that the system can support the appearance of quantum breathers, and discuss their existence conditions and properties. In addition, our results show that, for quantum breathers in this system, both the corresponding energy and magnetic moment are quantized.

scholarly journals Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Charles B. Thorn
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Spin Chain ◽  
Discrete Dynamical System ◽  
Heisenberg Spin ◽  
Free Fermions ◽  
Heisenberg Spin Chain ◽  
Delta Sigma ◽  
Special Cases ◽  
Quantized String

Abstract Although the energy spectrum of the Heisenberg spin chain on a circle defined by$$ H=\frac{1}{4}\sum \limits_{k=1}^M\left({\sigma}_k^x{\sigma}_{k+1}^x+{\sigma}_k^y{\sigma}_{k+1}^y+\Delta {\sigma}_k^z{\sigma}_{k+1}^z\right) $$ H = 1 4 ∑ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether M ∈ 4ℕ + r, where r = −1, 0, 1, 2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M1< M and M − M1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case ∆ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R0. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for ∆ ≠ 0 is a change in the compactification radius R0→ R∆. As ∆ → −1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.

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