  In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic
triangular Heisenberg antiferromagnets, high-energy states carrying
considerable spectral weights have been observed in a magnetic field using
inelastic neutron scattering. Such high-energy properties cannot be explained
in terms of either Nambu-Goldstone bosons due to spontaneous breaking of
continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here,
we show that the mechanism causing the high-energy states is analogous to that
of the upper Hubbard band in the one-dimensional Hubbard model, by
theoretically tracing the origin of the high-energy states back to string
solutions of the Bethe ansatz.
