Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases

Abstract

We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wavefunctions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U($1$) gauge anomaly.

16 pages. v2: small corrections and added references; rearranged final discussion; added material about multicomponent generalization: now 19 pages

References in corpus (6)

• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Thermal Hall Effect and Geometry with Torsion
• Low-energy effective theory in the bulk for transport in a topological phase
• Density-curvature response and gravitational anomaly
• Geometry of Fractional Quantum Hall Fluids
• FQHE on curved backgrounds, free fields and large N

Cited by in corpus (20)

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• Quantum Field Theory Anomalies in Condensed Matter Physics
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Effective action approach to the filling anomaly in crystalline topological matter
• Anisotropic Quantum Hall Droplets
• Thomas Precession for Dressed Particles
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Quantum Hall States and Conformal Field Theory on a Singular Surface
• A numerical study of bounds in the correlations of fractional quantum Hall states
• Geometry and large N limits in Laughlin states
• Geometric test for topological states of matter
• Electrons and composite Dirac fermions in the lowest Landau level
• Adiabatic Deformations of Quantum Hall Droplets
• Geometric and computational aspects of chiral topological quantum matter
• Fractional quantum Hall interface induced by geometric singularity