An emergent geometric description for a topological phase transition in the Kitaev superconductor model

摘要

Resorting to Wilsonian renormalization group (RG) transformations, we proposean emergent geometric description for a topological phase transition in theKitaev superconductor model. An effective field theory consists of an emergentbulk action with an extra dimension, an ultraviolet (UV) boundary condition foran initial value of a coupling function, and an infrared (IR) effective actionwith a fully renormalized coupling function. The bulk action describes theevolution of the coupling function along the direction of the extra dimension,where the extra dimension is identified with an RG scale and the resultingequation of motion is nothing but a $\beta-$function. In particular, the IReffective field theory turns out to be consistent with a Callan-Symanzikequation which takes into account both the bulk and IR boundary contributions.This derived Callan-Symanzik equation gives rise to a metric structure. Basedon this emergent metric tensor, we uncover the equivalence of the entanglemententropy between the emergent geometric description and the quantum field theoryin the vicinity of the quantum critical point.