Geometry of Fractional Quantum Hall Fluids

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.

New expanded version. 11 pages, 53 references, expnaded and improved presentation. Published version

References in corpus (4)

• Density-curvature response and gravitational anomaly
• "Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids
• Hall viscosity from effective field theory
• Modular transformation and bosonic/fermionic topological orders in Abelian fractional quantum Hall states

Cited by in corpus (14)

• Spacetime Symmetries of the Quantum Hall Effect
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Theory of Nematic Fractional Quantum Hall State
• General coordinate invariance in quantum many-body systems
• Particle-hole symmetry and electromagnetic response of a half-filled Landau level
• More On Nonrelativistic Diffeomorphism Invariance
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Ward Identities for Hall Transport
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• Composite anyons on a torus
• Covariant Poisson's equation in torsional Newton-Cartan gravity
• Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories