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 TMF, 1973, Volume 15, Number 1, Pages 120–126 (Mi tmf3647)

Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction

I. G. Gochev

Abstract: The two-magnon problem is solved for a chain of spins $s=1/2$ with allowance for the interaction of neighbors that come after the nearest neighbors. It is shown that for any interaetion of the second neighbors (all the interactions are ferromagnetic) a bound state of two spin waves exists for all $k$, $0<k<\pi$ ($k$ is the center of mass momentum of the system of two magnons). For $k=\pi$ a sufficiently strong interaction of the second neighbors destroys the bound state, and this result eonfirms the results of [3, 4].

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English version:
Theoretical and Mathematical Physics, 1973, 15:1, 402–406

Citation: I. G. Gochev, “Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction”, TMF, 15:1 (1973), 120–126; Theoret. and Math. Phys., 15:1 (1973), 402–406

Citation in format AMSBIB
\Bibitem{Goc73} \by I.~G.~Gochev \paper Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction \jour TMF \yr 1973 \vol 15 \issue 1 \pages 120--126 \mathnet{http://mi.mathnet.ru/tmf3647} \transl \jour Theoret. and Math. Phys. \yr 1973 \vol 15 \issue 1 \pages 402--406 \crossref{https://doi.org/10.1007/BF01028269} 

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This publication is cited in the following articles:
1. I. G. Gochev, “Bound magnon-exciton states”, Theoret. and Math. Phys., 22:3 (1975), 290–293
2. S. M. Tashpulatov, “Exploration of spectrum of the energy operator of two-magnon system in the one-dimensional anisotropic Heisenberg ferromagnet with interaction of second neighbours”, Theoret. and Math. Phys., 107:1 (1996), 544–549
3. S. M. Tashpulatov, “Two-magnon systems in the one-dimensional non-Heisenberg ferromagnet with nearest neighbours and second nearest neighbours interaction with spin value $s=1$”, Theoret. and Math. Phys., 107:2 (1996), 620–628
4. S. M. Tashpulatov, “Spectra and bound states of the energy operator of two-magnon systems in a non-Heisenberg ferromagnet with spin one and nearest-neighbor coupling”, Theoret. and Math. Phys., 125:2 (2000), 1539–1551
5. Tashpulatov, SM, “SPECTRA AND BOUND STATES OF THE ENERGY OPERATOR OF TWO-MAGNON SYSTEM IN A NON-Heisenberg FERROMAGNET WITH SPIN S=3/2 AND NEAREST-NEIGHBOR INTERACTIONS”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 12:1 (2009), 117
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