Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E ₈ 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 CoNb 2 O 6 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.

Suppression of magnetic ordering in quasi-one-dimensional FexCo1−xNbSarvezuk1, Kinast2, Colin3 et al. 2011Phys. Rev. B

“…Indeed, as nicely discussed in Ref. 13, a magnetic field applied parallel to the Ising spins induces a gap to the kink excitations that otherwise would suppress ferromagnetic order at finite temperature for free chains.…”

“…10 The magnetic phase diagram of CoNb 2 O 6 was investigated combining powder and single crystal neutron diffraction by Schärf et al, 9 and later by Heid et al 3,4 and Kobayashi et al 5 This system has also been studied by nuclear magnetic resonance (NMR), 11,12 electron-spin resonance (ESR), 11 and infrared-transmission spectroscopy. 12 Recently, quantum-critical behavior consistent with the transverse-field Ising model in one dimension and exotic-symmetry excitations were observed 13 by inelastic neutron scattering on a single crystal of CoNb 2 O 6 . This experimental study was followed by a theoretical investigation of the interplay between quantum criticality and geometric frustration in the same system, still in the presence of a transverse magnetic field.…”

Quantum critical behavior in the asymptotic limit of high disorder in the medium entropy alloy NiCoCr0.8

“…[1][2][3][4][5] One key to making progress in this area is the identification of model material systems that are complex enough to exhibit the physics of interest but simple enough to be compared to theory. Studies of several low dimensional magnetic materials have greatly improved our understanding of QCP physics in insulating solids, [6][7][8] but our understanding of QCP phenomena in metallic systems is much less clear. 2,9,10 One hindrance is that few systems are microscopically homogeneous near the QCP, due to the need for small concentrations of dopants, and this can disrupt the feedback loop between theory and experiment.…”

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO4

“…Their detection, however, remains a central challenge for condensed matter physics [6], and relies on the presence of quantum entanglement in their ground state and fractional quasiparticles in their excitation spectra. While the former can be checked by numerics [7], the latter can be experimentally detected by thermodynamic techniques [8][9][10] or spectroscopic probes such as inelastic neutron scattering [11][12][13][14][15][16][17] and electronspin resonance [18][19][20][21].…”