Quantum Hall States and Conformal Field Theory on a Singular Surface
arXiv:1709.04397 · doi:10.1088/1751-8121/aa91dc
Abstract
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone [Cardy, Peschel 1988], and the known results for critical systems on polyhedra and flat branched Riemann surfaces.
arXiv commentv1: 55 pages, 2 figures, v2: minor edits - invited contribution to a special issue of J. Phys. A for John Cardy's 70th birthday
References in corpus (22)
- Entanglement Entropy and Quantum Field Theory
- Synthetic Landau levels for photons
- Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
- On the definition of a unique effective temperature for non-equilibrium critical systems
- Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
- Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
- Large N expansion for the 2D Dyson gas
- Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
- Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
- Geometric adiabatic transport in quantum Hall states
- Quantum Hall effect and Quillen metric
- Effective action in spherical domains
- FQHE on curved backgrounds, free fields and large N
- Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
- On Functional Determinants of Laplacians in Polygons and Simplices
- Collective Field Theory for Quantum Hall States
- On the Moduli Space of Singular Euclidean Surfaces
- Adiabatic Quantum Transport: Quantization and Fluctuations
- Geometric Defects in Quantum Hall States
- Further results on Functional Determinants of Laplacians in Simplicial Complexes
- Spectral analysis and zeta determinant on the deformed spheres
- Geometry and large N limits in Laughlin states
Cited by in corpus (5)
- Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
- Multipartite entanglement in two-dimensional chiral topological liquids
- Laughlin states on higher genus Riemann surfaces
- Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
- Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces