2014/06/30 by Gil Young Cho, Yizhi You, Eduardo Fradkin · 81 citations
Mathematics · Physics and Astronomy · #Abelian group #Classical mechanics #Connection (principal bundle) #Curvature #Gaussian curvature #Geometry #Magnetic field #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Spin (aerodynamics) #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.90.115139
published in Physical Review B 90(11) (American Physical Society) · New expanded version. 11 pages, 53 references, expnaded and improved presentation. Published version
openalex publication_date 2014/09/22 · arxiv created 2014/09/29 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e., the Hall viscosity, and the Wen-Zee term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. We derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both Abelian and non-Abelian states.