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The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonianand external magnetic fields exceeding the saturation field Bs is considered.We show that the problem can be exactly mapped onto an effective tight-bindingimpurity problem. It allows to obtain explicit exact expressions for thetwo-magnon Green's functions for arbitrary dimension and number ofinteractions. We apply this theory to a quasi-one dimensional helimagnet withferromagnetic nearest neighbor J1 < 0 and antiferromagnetic next-nearestneighbor J2 > 0 interactions. An outstanding feature of the excitation spectrumis the existence of two-magnon bound states. This leads to deviations of thesaturation field Bs from its classical value Bs(classical) which coincides withthe one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661the minimum of the two-magnon spectrum occurs at the boundary of the Brillouinzone. Based on the two-magnon approach, we propose general analytic expressionsfor the saturation field Bs, confirming known previous results forone-dimensional isotropic systems, but explore also the role of interchain andlong-ranged intrachain interactions as well as of the exchange anisotropy.Comment: 21 pages, 6 Figures. submitted to Phys. Rev.

Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field