On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6

In a recent paper Coldea et al (2010 Science {\bf 327} 177) report observation of the weak confinement of kinks in the Ising spin chain ferromagnet CoNb2O6 at low temperatures. To interpret the entire spectra of magnetic excitations measured via neutron scattering, they introduce a phenomenological model, which takes into account only the two-kink configurations of the spin chain. We present the exact solution of this model. The explicit expressions for the two-kink bound-state energy spectra and for the relative intensities of neutron scattering on these magnetic modes are obtained in terms of the Bessel function.Comment: 18 pages, 9 figures; v2: figures 1,3,4 replaced, few misprints correcte

Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry

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.Comment: 18 pages with embedded figure