  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.
