Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry

Abstract

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb2O6 through its critical point using strong transverse magnetic fields. The spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean as predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviours.

18 pages with embedded figures

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• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Ab-initio study of structural, elastic, electronic, optical and thermodynamic properties of MgV2O6
• Quantized ΔS=2 Excitation Spectra by Confinement in an S=1 Spin Chain
• The Toda-Weyl mass spectrum
• Engineering a Josephson junction chain for the simulation of the clock model
• Properties of an organic model $S=1$ Haldane chain system
• A Mathematical Model for the Genetic Code(s) Based on Fibonacci Numbers and their q-Analogues
• From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality
• Fitness landscape for quantum state tomography from neutron scattering
• Random transverse and longitudinal field Ising chains
• Applied-field magnetic structure and spectroscopy shifts of the effective spin-$\frac{1}{2}$, $XY$-like magnet Li${}_2$CoCl${}_4$
• A Shielding Property for Thermal Equilibrium States on the Quantum Ising Model
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• Spin amplification in realistic systems
• Exactly Solvable Phase Transition in a Cavity-Coupled 1D Ising Chain
• Ising spin ladders of orthopyroxene CoGeO${}_3$
• Amplified response of cavity-coupled quantum-critical systems
• Quantum critical behavior of diluted quasi-one-dimensional Ising chains
• Dynamics of Quantum Chiral Solitons
• Extremely Large Magnetic Entropy Changes, Quantum Phases, Transitions and Diagram in Gd(OH)3 Single Crystal Nanowires - Quasi-1D Large Spin (S = -7/2) Chain Antiferromagnet
• Magnetoelastic coupling at the field-induced transition in EuAl${}_{12}$O${}_{19}$
• On ground state phases of quantum spin systems
• Temperature driven false vacuum decay in coherently coupled Bose superfluids
• An integrated theoretical and numerical approach to understand modern experiments on quantum magnetism
• Periodic dynamics in an Ising chain with a quadratic transverse field
• Weyl orbit particles
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering
• Quantum Supercritical Crossover with Dynamical Singularity
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder
• Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields
• Dynamical correlation functions in the Ising field theory
• Unavoidable golden ratio
• Emergent $D_8^{(1)}$ spectrum and topological soliton excitation in CoNb${}_2$O${}_6$
• Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions
• Field-induced spin-structural transition and giant magnetostriction in Ising chain $\alpha$-CoV${}_2$O${}_6$
• Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids
• Few remarks on the mass spectrum of two-dimensional Toda lattice of $E_8$ type
• Exceptional Lattice Green's Functions
• Nonlocal pseudospin dynamics in a quantum Ising chain
• Relativistic meson spectra on ion-trap quantum simulators
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems