John Chalker

Abstract:

We show numerically that the “deconfined” quantum critical point between the Neel antiferromagnet ´ and the columnar valence-bond solid, for a square lattice of spin 1=2, has an emergent SO(5) symmetry. This symmetry allows the Neel vector and the valence-bond solid order parameter to be rotated into each ´ other. It is a remarkable (2 þ 1)-dimensional analogue of the SOð4Þ¼½SUð2Þ × SUð2Þ=Z2 symmetry that appears in the scaling limit for the spin-1=2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2 þ 1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP1 model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.

Abstract:

Motivated by recent synthesis of the hyperhoneycomb material β−Li2IrO3, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalized degrees of freedom are Majorana fermions and emergent flux loops. The properties of this 3D model are known to differ in important ways from those of its 2D counterpart—it has a finite-temperature phase transition, as well as distinct features in the Raman response. We show, however, that the qualitative behavior of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.