Spin dynamics of the $E_8$ particles

In this article, we report on inelastic neutron scattering measurements on a quasi-1D antiferromagnet BaCo${}_2$V${}_2$O${}_8$ under a transverse magnetic field applied along the (0,1,0) direction. Combining results of inelastic neutron scattering experiments, analytical analysis, and numerical simulations, we precisely studied the $E_8$ excitations appearing in the whole Brillouin zone at $B_c^{1D}\approx 4.7$ T. The energy scan at $Q=(0,0,2)$ reveals a match between the data and the theoretical prediction of energies of multiple $E_8$ excitations. Furthermore, dispersions of the lightest three $E_8$ particles have been clearly observed, confirming the existence of the $E_8$ particles in BaCo${}_2$V${}_2$O${}_8$. Our results lay down a concrete ground to systematically study the physics of the exotic $E_8$ particles.