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

TL;DR

This paper derives exact two-magnon excitation spectra for frustrated helimagnets above their saturation field, revealing bound states and providing explicit formulas for the saturation field considering various interactions.

Contribution

It introduces an exact mapping of the two-magnon problem to a tight-binding impurity model and derives explicit Green's function expressions for arbitrary dimensions.

Findings

Existence of two-magnon bound states in the spectrum.

Explicit formulas for the saturation magnetic field Bs.

Role of interchain, long-range interactions, and anisotropy in excitation spectra.

Abstract

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 Bs(classical) which coincides with the one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661 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.