(E_8\) Spectra of Quasi-one-dimensional Antiferromagnet BaCo\(_2\)V\(_2\)O\(_8\) under Transverse Field

We report \(^{51}\)V nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo\(_2\)V\(_2\)O\(_8\) under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the N\'{e}el temperatures unveils a 1D quantum critical point (QCP) at \(H_c^{1D}\approx 4.7\) T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at \(H_c^{1D}\) is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional \(E_8\) Lie algebra. These excitations keep to be non-diffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive \(E_8\) phase in the compound, and open new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.