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We report $^{51}$V nuclear magnetic resonance (NMR) and inelastic neutronscattering (INS) measurements on a quasi-1D antiferromagnet BaCo$_2$V$_2$O$_8$under transverse field along the [010] direction. The scaling behavior of thespin-lattice relaxation rate above the N\'{e}el temperatures unveils a 1Dquantum critical point (QCP) at $H_c^{1D}\approx 4.7$ T, which is masked by the3D magnetic order. With the aid of accurate analytical analysis and numericalcalculations, we show that the zone center INS spectrum at $H_c^{1D}$ isprecisely described by the pattern of the 1D quantum Ising model in a magneticfield, a class of universality described in terms of the exceptional $E_8$ Liealgebra. These excitations keep to be non-diffusive over a certain field rangewhen the system is away from the 1D QCP. Our results provide an unambiguousexperimental realization of the massive $E_8$ phase in the compound, and opennew experimental route for exploring the dynamics of quantum integrable systemsas well as physics beyond integrability.

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