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

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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]. 
@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},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a9/}
}
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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/