  Complex bound states of magnetic excitations, known as Bethe string, were
predicted almost a century ago to exist in one-dimensional quantum magnets 1.
The dispersions of the string states have so far remained the subject of
intensive theoretical studies 2-7. By performing neutron scattering experiments
on the one-dimensional Heisenberg-Ising antiferromagnet SrCo2V2O8 in high
longitudinal magnetic fields, we reveal in detail the dispersion relations of
the string states over the full Brillouin zone, as well as their magnetic field
dependences. Furthermore the characteristic energy, the scattering intensity
and linewidth of the observed string states exhibit excellent agreement with
our precise Bethe Ansatz calculations. Our results establish the important role
of string states in the quantum spin dynamics of one-dimensional systems, and
will invoke studies of their dynamical properties in more general many-body
systems.
