Almost a century ago, string states-complex bound states of magnetic excitations-were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCoVO in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe's result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

The quantum adiabatic theorem plays an important role in quantum mechanics. However, counter-examples were produced recently, indicating that their transition probabilities do not converge as predicted by the adiabatic theorem [K. P. Marzlin et al., Phys. Rev. Lett. 93, 160408 (2004); D. M. Tong et al., Phys. Rev. Lett. 95, 110407 (2005)]. For a special class of Hamiltonians, we examine the standard criterion for adiabatic evolution experimentally and theoretically, as well as three newly suggested adiabatic conditions. We show that the standard criterion is neither sufficient nor necessary.

We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound BaCo2V2O8 as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below TN ≃ 5.5 K. In a field-induced gapless phase above Bc = 3.8 T, we identify many-body string excitations as well as low-energy fractional psinon/antipsinon excitations by comparing to Bethe-Ansatz calculations. In the vicinity of Bc, the high-energy string excitations are found to be dynamically dominant over the fractional excitations.

Near the transverse-field induced quantum critical point of the Ising chain, an exotic dynamic spectrum consisting of exactly eight particles was predicted, which is uniquely described by an emergent quantum integrable field theory with the symmetry of the E8 Lie algebra, but rarely explored experimentally. Here we use high-resolution terahertz spectroscopy to resolve quantum spin dynamics of the quasi-one-dimensional Ising antiferromagnet BaCo2V2O8 in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify E8 particles as well as their two-particle excitations.