Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry

By R. Coldea, D. Tennant, E. Wheeler, E. Wawrzyńska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, K. Kiefer. Science, 2010

684 citations recorded by the source corpus.

Hidden Symmetry Revealed It is not often that an exact theory can describe a many-particle quantum-mechanical system, but one of the few exceptions is the behavior of a string of ferromagnets—an Ising chain—at magnetic field strengths that separate different types of ordering. Its excitations were predicted 20 years ago to be governed by the symmetry group E8, one of the most intriguing objects in mathematics. Now, Coldea et al. (p. 177) report direct experimental confirmation of this result in a quasi-one-dimensional Ising ferromagnet CoNb2O6, which they probed by neutron scattering. Two of the eight predicted excitations could be observed. Moreover, the ratio of the two lowest excitations is in quantitative agreement with the so-called “golden ratio” predicted by theory. A long-predicted hidden symmetry in spin ordering has been observed experimentally at temperatures near absolute zero. 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 eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi–one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. 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 predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/0e5a910fd6538e9e2a5768bacfa637314e5e1a4d

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Citations in the corpus

Fermi gases in one dimension: From Bethe ansatz to experiments (2013, background): “Such exotic quantum symmetry in the excitation spectrum was observed in a recent experiment in the traditional setting of condensed matter physics (Coldea et al., 2010).”
Geometry of quantum phase transitions (2019, background): “The dynamical susceptibility is a well studied quantity which has been observed experimentally in a wide variety of materials [339, 340, 341, 342, 343, 344].”
Colloquium: Spontaneous magnon decays (2012, background): “In a different context, similar distortion of the excitation curve εk in the vicinity of the continuum boundary was also observed by Coldea et al. (2010).”