Experimental observation of quantum many-body excitations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>E</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math> symmetry in the Ising chain ferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CoNb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>
Kirill Amelin, Johannes Engelmayer, J. Viirok, U. Nagel, T. Rõõm, T. Lorenz, Zhe Wang
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 ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six ${E}_{8}$ particles, ${\mathrm{m}}_{1}$ to ${\mathrm{m}}_{6}$, and the two-particle $({\mathrm{m}}_{1}+{\mathrm{m}}_{2})$ continuum in an applied transverse magnetic field of ${B}_{c}^{\text{1D}}=4.75 \mathrm{T}$, before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles $({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})$ above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.