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

The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field B(s) is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one-dimensional helimagnet with ferromagnetic nearest-neighbor J(1) < 0 and antiferromagnetic next-nearest neighbor J(2) > 0 interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field B(s) from its classical value Bs cl which coincides with the one-magnon instability. For the refined frustration ratio vertical bar J(2)/J(1)vertical bar > 0.374 661 the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field B(s), confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.