Quantum mechanics and quantum Hall effect on Riemann surfaces

Abstract

The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of the $\theta$-bundle, and the wave functions of the Landau levels in the case of the the Poincar{\' e} metric. The degeneracy of the the Landau levels is obtained by using the Riemann-Roch theorem. Then we construct the Laughlin wave function on Riemann surfaces and discuss the mathematical structure hidden in the Laughlin wave function. Moreover the degeneracy of the Laughlin states is also discussed.

24 pages, Latex

References in corpus (1)

• Hierarchical Wave Functions of Fractional Quantum Hall Effect on the Torus

Cited by in corpus (34)

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• Geometric effects on critical behaviours of the Ising model
• FQHE on curved backgrounds, free fields and large N
• Quantum mechanics on noncommutative Riemann surfaces
• Quantum Hall Effect on Higher Dimensional Spaces
• Fractional charge and inter-Landau level states at points of singular curvature
• Geometric Defects in Quantum Hall States
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
• Hyperbolic Supersymmetric Quantum Hall Effect
• Explicit monodromy of Moore-Read wave functions on a torus
• Landau Levels in the noncommutative $Ad{S}_2$
• Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
• Supersymmetry-based Approach to Quantum Particle Dynamics
• Quantum Hall effect on the Lobachevsky plane
• Haldane's Fractional Statistics and the Riemann-Roch Theorem
• Scalar Curvature Factor in the Schroedinger Equation and Scattering on a Curved Surface
• Coulomb gas representation of quantum Hall effect on Riemann surfaces
• A Quantum Ring in a Nanosphere
• Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics
• Laughlin states on higher genus Riemann surfaces
• Laughlin states on the Poincare half-plane and its quantum group symmetry
• Gravitational Response of Topological Quantum States of Matter
• Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces
• Integrable sigma models on Riemann surfaces
• Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
• Geometry and large N limits in Laughlin states
• Topologically Nontrivial Sectors of the Maxwell Field Theory on Algebraic Curves
• The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann Sphere
• Notes on the Squashed Sphere Lowest Landau Level
• Hierarchical Wave Functions Revisited