Condensed Matter Physics Seminar

We will present a simple understanding of universal geometric responses of fractional quantum Hall fluids to geometric deformations in which the fluids are living. In this talk, we will start with a pedagogical introduction/review of flux attachment/composite particle theories of fractional Quantum Hall States and the geometric responses of the fluids. Then we use the field theory descriptions 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. The field theoretic approaches successfully derive the spin `S' of the topological phases (which is the coefficient of Wen-Zee term), and thus we provide consistent and complete understanding of the abelian topological phases which are completely characterized by K-matrix, q-vector, and S-vector in Wen's hydrodynamic descriptions of the phases.