Collective Field Theory for Quantum Hall States
arXiv:1412.8716 · doi:10.1103/PhysRevB.92.235141
Abstract
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a (filling fraction dependent) background charge. Gradient corrections to the Gaussian field theory arise from ultraviolet regularization. They are the origin of the gravitational anomaly and are described by the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
v1: 20 pages; v2: 6 pages, considerably revised and rewritten for the sake of clarity and brevity, v3: 7 pages, updated to reflect the published version which includes a discussion of the effects spin
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- Particle-Hole Duality in the Lowest Landau Level
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- Free surface variational principle for an incompressible fluid with odd viscosity
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- Lowest Landau level on a cone and zeta determinants
- Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly
- Geometric responses of the Pfaffian state
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- Quantum Hall States and Conformal Field Theory on a Singular Surface
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- Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
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- Phase space holography with no strings attached
- Topological defects in the Liouville field theories with different cosmological constants
- Liouville perturbation theory for Laughlin state and Coulomb gas
- Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics