Quantum criticality and confinement effects in an Ising chain in transverse field

The Ising chain in transverse field is one of the key paradigms for the theory of continuous zero-temperature quantum phase transitions. We have recently realized this system experimentally by applying strong magnetic fields to the quasi- 1D, low-exchange Ising ferromagnet CoNb2O6 to drive it to its quantum critical point where the spontaneous long-range magnetic order is suppressed by magnetic field [1]. Using high-resolution single-crystal neutron scattering we have probed how the spin dynamics evolves with the applied field and have observed a dramatic change in the character of spin excitations at the quantum critical point, from pairs of domain-wall (kink) quasiparticles in the magnetically-ordered phase, to sharp spin- flip quasiparticles in the paramagnetic phase. The weak, but finite couplings between the chains significantly enrich the physics by stabilizing a complex structure of two-kink bound states due to mean-field confinement effects. In zero field the rich spectrum of bound states can be quantitatitively understood following McCoy and Wu's analytic theory of weak confinement [2]. Just below the critical field the energies of the two lowest bound states approach the ``golden ratio'' as predicted by Zamolodchikov's E8 scaling limit solution of the off-critical Ising model in a weak longitudinal field [3]. \\[4pt] [1] R. Coldea, D.A. Tennant, E.M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, K. Kiefer, Science 327, 177 (2010).\\[0pt] [2] B. M. McCoy and T. T. Wu, Phys. Rev. D 18, 1259 (1978).\\[0pt] [3] A.B. Zamolodchikov, Int. J. Mod. Phys. A4, 4235 (1989).