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

Abstract

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 Néel 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.

6 pages, 4 figures. Supplemental Material is in other format