2016/10/31 by Ki-Seok Kim, Ki‐Seok Kim, Miok Park +2 · 24 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Black Holes and Theoretical Physics #Effective action #Mathematics #Phase transition #Physics #Quantum #Quantum entanglement #Quantum field theory #Quantum many-body systems #Quantum mechanics #Renormalization group #Superconductivity #Theoretical physics #Topology (electrical circuits) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevd.96.086015
published in Physical review. D/Physical review. D. 96(8) (American Physical Society) · Two figures added
arxiv created 2017/09/09 · openalex publication_date 2017/10/23 · arxiv updated 2017/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Resorting to Wilsonian renormalization group (RG) transformations, we propose an emergent geometric description for a topological phase transition in the Kitaev superconductor model. An effective field theory consists of an emergent bulk action with an extra dimension, an ultraviolet (UV) boundary condition for an initial value of a coupling function, and an infrared (IR) effective action with a fully renormalized coupling function. The bulk action describes the evolution of the coupling function along the direction of the extra dimension, where the extra dimension is identified with an RG scale and the resulting equation of motion is nothing but a β-function. In particular, the IR effective field theory turns out to be consistent with a Callan-Symanzik equation which takes into account both the bulk and IR boundary contributions. This derived Callan-Symanzik equation gives rise to a metric structure. Based on this emergent metric tensor, we uncover the equivalence of the entanglement entropy between the emergent geometric description and the quantum field theory in the vicinity of the quantum critical point.