Dispersions of many-body Bethe strings

Complex bound states of magnetic excitations, known as Bethe strings, 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 intense theoretical studies(2-7). Here, 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 dependencies. 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. In one-dimensional quantum magnets, complex bound states of magnetic excitations known as Bethe strings have long been predicted. Now, a detailed neutron scattering study of SrCo2V2O8 reveals their magnetic-field-dependent dispersion relation.