Fractional quantum Hall states of bosons on cones

TL;DR

This paper investigates fractional quantum Hall states of bosons on conical geometries, constructing trial wave functions, comparing with exact results, and analyzing density profiles to understand universal properties influenced by curvature.

Contribution

It introduces new trial wave functions for bosonic quantum Hall states on cones and compares them with exact diagonalization, advancing understanding of geometric effects on quantum Hall physics.

Findings

Density profiles reflect universal quantum Hall properties.

Numerical results agree with analytical predictions.

Conical curvature modifies local density distributions.

Abstract

Motivated by a recent experiment which synthesizes Landau levels for photons on cones [Schine {\em et al.}, Nature 534, 671 (2016)], and more generally the interest in understanding gravitational responses of quantum Hall states, we study fractional quantum Hall states of bosons on cones. A variety of trial wave functions for conical systems are constructed and compared with exact diagonalization results. The tip of a cone is a localized geometrical defect with singular curvature which can modify the density profiles of quantum Hall states. The density profiles on cones can be used to extract some universal information about quantum Hall states. The values of certain quantities are computed numerically using the density profiles of some quantum Hall states and they agree with analytical predictions.