Lowest Landau level on a cone and zeta determinants

Abstract

We consider the integer QH state on Riemann surfaces with conical singularities, with the main objective of detecting the effect of the gravitational anomaly directly from the form of the wave function on a singular geometry. We suggest the formula expressing the normalisation factor of the holomorphic state in terms of the regularized zeta determinant on conical surfaces and check this relation for some model geometries. We also comment on possible extensions of this result to the fractional QH states.

15 pages

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Cited by in corpus (15)

• Bimetric Theory of Fractional Quantum Hall States
• Ideal Chern bands are Landau levels in curved space
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Probing topological superconductors with emergent gravity
• Chern Insulators on Singular Geometries
• Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
• Laughlin states on higher genus Riemann surfaces
• On Determinants of Laplacians on Compact Riemann Surfaces Equipped with Pullbacks of Conical Metrics by Meromorphic Functions
• Determinant of Friederichs Dirichlet Laplacians on $2$-dimensional hyperbolic cones
• Spectral determinant on Euclidean isosceles triangle envelopes of fixed area as a function of angles: absolute minimum and small-angle asymptotics
• Metrics of constant positive curvature with conical singularities, Hurwitz spaces, and $\det \Delta$
• Fractional quantum numbers via complex orbifolds
• Determinants of Laplacians for constant curvature metrics with three conical singularities on 2-sphere
• Polyakov formulas for conical singularities in two dimensions
• The variation of Barnes and Bessel zeta functions