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 Bₛ 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 J₁<0 and antiferromagnetic next-nearest neighbor J₂>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 Bₛ from its classical value Bₛᶜˡ which coincides with the one-magnon instability. For the refined frustration ratio J₂∕J₁>0.3740.2em0ex661 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 Bₛ, 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.