Quantum Hall States and Conformal Field Theory on a Singular Surface

TL;DR

This paper explores the emergent conformal symmetry in quantum Hall states on singular surfaces, connecting geometric transport properties with conformal field theory and extending finite-size correction results to hyperbolic geometries.

Contribution

It develops the understanding of conformal symmetry in quantum Hall states on singular surfaces and computes universal finite-size corrections on hyperbolic spheres with singularities.

Findings

Emergent conformal symmetry in quantum Hall states on singular surfaces.

Universal finite-size corrections for critical systems on hyperbolic spheres with singularities.

Connection between geometric transport and conformal dimensions of primary fields.

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.