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

References in corpus (3)

• "Deconfined" quantum critical points
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• Energy spectrum of bound-spinons in the quantum Ising spin-chain ferromagnet

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• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Spin amplification in realistic systems
• 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
• On ground state phases of quantum spin systems
• Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering
• Relativistic meson spectra on ion-trap quantum simulators
• Weyl orbit particles
• Periodic dynamics in an Ising chain with a quadratic transverse field
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder
• A Shielding Property for Thermal Equilibrium States on the Quantum Ising Model
• Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids
• Emergent $D_8^{(1)}$ spectrum and topological soliton excitation in CoNb${}_2$O${}_6$
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• Few remarks on the mass spectrum of two-dimensional Toda lattice of $E_8$ type
• Quantum Supercritical Crossover with Dynamical Singularity
• An integrated theoretical and numerical approach to understand modern experiments on quantum magnetism
• Temperature driven false vacuum decay in coherently coupled Bose superfluids
• Exceptional Lattice Green's Functions
• Unavoidable golden ratio
• Magnetoelastic coupling at the field-induced transition in EuAl${}_{12}$O${}_{19}$
• Dynamics of Quantum Chiral Solitons