Excitations for the one-dimensional S = 1 pseudo-Heisenberg antiferromagnetic chain
Elena V. Orlenko, Fedor E. Orlenko, George G. Zegrya
DOI: 10.4236/ns.2010.211155   PDF   HTML     4,837 Downloads   9,462 Views   Citations


We are interested in the anisotropic S=1 antiferromagnetic chain. System of particles with an arbitrary spin is described directly from the first principles, based on the symmetry law. The ground state of the one-dimensional S=1 pseudo-Heisenberg antiferromagnet with single-ion anisotropy is calculated. Excitations of the chain in the form of nonlinear spin waves and, in particular, the possibility of a soliton solution is considered.

Share and Cite:

Orlenko, E. , Orlenko, F. and Zegrya, G. (2010) Excitations for the one-dimensional S = 1 pseudo-Heisenberg antiferromagnetic chain. Natural Science, 2, 1287-1291. doi: 10.4236/ns.2010.211155.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Ho, T.L. and Yip, L. (2000) Fragmented and single condensate ground ststes of spin-1 Bose gas. Physical Review Letters, 84, 4031-4034.
[2] Haldane F.D.M. (1983) Phase diagrams of F=2 spinor Bose-Einstein condensates. Physical Review A, 50, 1153.
[3] Haldane F.D.M. (1983) Physical Letters, 93A, 464.
[4] Ciobanu, C.V., Yip, S.K. and Ho, T.-L. (2000) Phase diagrams of F=2 spinor Bose-Einstein condensates. Physical Review A, 61, 1050-1056.
[5] Ho, T.-L. (1998) Bose-einstein condensate in optical traps. Physical Review Letters, 81, 742-745.
[6] Orlenko, E. (2007) The universal Hamiltonian of the exchange interaction for the system of particles with an arbitrary spin. International Journal of Quantum Chemistry, 107, 2838-2843.
[7] Albuquerque, A., Hamer, F., Chris, J. and Jaan, O.(2009) Quantum phase diagram and excitations for the one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy. Physical Review B, 79, 054412.
[8] Affleck, I., Kennedy, T., Lieb, E.H. and Tasaki, H. (1987) Rigorous results on valence-bond ground states in antiferromagnets. Physical Review Letters, 59, 799.
[9] Schollw?ck, U., Jolicoeur, T. and Garel, T. (1996) Onset of incommensurability at the valence-bond-solid point in the S51 quantum spin chain. Physical Review B, 53, 3304.
[10] Orlenko, E., Mazets, I. and Matisov, B. (2003) Nonlinear magnetic phenomena in the Bose-Einstein condensate. Technical Physics, 48, 26-30.
[11] García-Ripoll, J.J., Martin-Delgado, M.A. and Cirac, J.I. (2004) Implementation of spin hamiltonians in optical lattices. Physical Review Letters, 93, 250405.
[12] Dalla Torre, E.G., Berg, E. and Altman, E. (2006). Hidden order in 1D bose insulators. Physical Review Letters, 97, 260401.
[13] den Nijs, M. and Rommelse, K. (1989) Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains. Physical Review B, 40, 4709.
[14] Busch Th and Anglin J R, (2001) Dark-bright solitons in inhomogeneous bose-einstein condensates. Physical Review Letters, 87, 010401.
[15] Trillo, S., Wabnitz, S., Wright, E.M. and Stegeman, G.I. (1988) Optical solitary waves induced by cross-phase modulation. Optics Letters, 13, 871-873.
[16] Christodoulides, D.N. (1988) Black and white vector solitons in weakly birefringeht optical fibers. Physical Letter A, 132, 451-452.
[17] Manakov, S.V. (1974) On the integrality and stochastic in the discrete dynamical systems. Zh. éksp. Teor. Fiz., 67, 543-555.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.