Experimental Observation of Quantum Many-Body Excitations of $E_8$ Symmetry in the Ising Chain Ferromagnet CoNb$_2$O$_6$

Abstract: Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the $E_8$ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb$_2$O$_6$. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six $E_8$ particles, $\mathbf{m}_1$ to $\mathbf{m}_6$, and the two-particle ($\mathbf{m}_1+\mathbf{m}_2$) continuum in an applied transverse magnetic field of $B_c^{1D}=4.75$ T, before the three-dimensional magnetic order is suppressed above $B_c^{3D}\approx 5.3$ T. The observation of the higher-energy particles ($\mathbf{m}_3$ to $\mathbf{m}_6$) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.