Magnons bound states

It should be noted, to begin with, that biphonons are quite analogous to bound states of two magnons (4)-(6). 

D fermion system to a 2-D classical Coulomb gas is employed to calculate the dynamical magnetic susceptibility of the 1-D fermion system. The result points towards the existence of bound magnon states in a 1-D fermion system. 

The latter puzzle may find its solution in a recent investigation of the spectrum of He- by Luther [7]. There it is shown that for A < 2 an increasing number of excitation branches appear below the fermion branch which is present for all values of A < 4. The states which correspond to these branches are to be viewed as bound spin-wave states in the model under consideration. From the equivalence of Hu and the Hamiltonian of the Sine-Gordon theory it can be inferred [7], [8] that the lowest bound magnon branch attains boson character as A approaches zero. In all probability hl represents the contribution... 

Table 11.4 shows that the 2 A+ state has a large transition dipole moment with the l Bfu state, and unlike the case for polyenes, it is not predominantly a pair of bound magnons, but a particle-hole excitation. (It is usually labelled the m Ag state.) This particle-hole excitation is either an n = 2 Mott-Wannier exciton, or the edge of the unbound particle-hole continuum. 

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