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

TL;DR

This study combines NMR and neutron scattering to observe the $E_8$ spectrum in a quasi-1D antiferromagnet, revealing a quantum critical point and the realization of the massive $E_8$ phase, advancing understanding of quantum integrable systems.

Contribution

It provides the first experimental realization of the $E_8$ spectrum in a quasi-1D antiferromagnet under a transverse field, linking experimental data with the 1D quantum Ising model.

Findings

Identification of a 1D quantum critical point at ~4.7 T.

Observation of $E_8$-related excitations in INS spectra.

Non-diffusive excitations away from the QCP.

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 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.