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.

Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the E 8 Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb 2 O 6. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E 8 particles, m 1 to m 6 , and the two-particle (m 1 + m 2) continuum in an applied transverse magnetic field of B 1D c = 4.75 T, before the three-dimensional magnetic order is suppressed above B 3D c ≈ 5.3 T. The observation of the higher-energy particles (m 3 to m 6) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

We measured absorption of THz radiation in YFeO 3 single crystals at a temperature of 3 K in the magnetic field up to 17 T applied in all three crystallographic directions. Two spin-wave modes were observed at the point with energies 1.2 meV (9.8 cm −1) and 2.4 meV (19.3 cm −1) in zero field. From the magnetic-field dependence of mode energies, we have refined the previously proposed model [S. E. Hahn et al., Phys. Rev. B 89, 014420 (2014)] and quantified the parameters of Dzyaloshinskii-Moriya interactions and single-ion anisotropies.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb$_2$O$_6$ and antiferromagnet BaCo$_2$V$_2$O$_8$ as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, $E_8$ dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.