Geometry of Fractional Quantum Hall Fluids

TL;DR

This paper derives the universal geometric responses of fractional quantum Hall fluids, such as Hall viscosity and Wen-Zee term, using Chern-Simons field theory and parton constructions, highlighting the role of background geometry coupling.

Contribution

It introduces a modified flux attachment concept to incorporate background geometry effects into Chern-Simons theories for fractional quantum Hall states.

Findings

Derived universal geometric response functions for FQH states.

Connected composite particle coupling to spin connection with geometric responses.

Unified description for abelian and non-abelian FQH states.

Abstract

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, the Wen-Zee term, and the gravitational Chern-Simons 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.