Geodesic
Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 120-126 
I. G. Gochev. Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 120-126. http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/
@article{TMF_1973_15_1_a9,
     author = {I. G. Gochev},
     title = {Two-magnon states in a one-dimensional {Heisenberg} model with second-neighbor interaction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {120--126},
     year = {1973},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/}
}
TY  - JOUR
AU  - I. G. Gochev
TI  - Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 120
EP  - 126
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/
LA  - ru
ID  - TMF_1973_15_1_a9
ER  - 
%0 Journal Article
%A I. G. Gochev
%T Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 120-126
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/
%G ru
%F TMF_1973_15_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

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$ 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].

[1] H. Bethe, Z. Physik, 71 (1931), 205 | DOI | Zbl

[2] M. Wortis, Phys. Rev., 132 (1963), 85 | DOI | MR

[3] C. Majumdar, J. Math. Phys., 10 (1969), 177 | DOI | MR

[4] I. Ono, S. Mikado, T. Oguchi, J. Phys. Soc. Japan, 30 (1971), 358 | DOI

[5] N. Fukuda, M. Wortis, J. Phys. Chem. Sol., 24 (1963), 1675 | DOI