Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge

Abstract

We give a microscopic derivation of the chiral Luttinger liquid theory for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from chiral Luttinger liquid theory one needs to go beyond Laughlin's approximation. We show that in the large N limit the IDLS is described by the dispersionless Toda hierarchy.

arXiv comment5 pages, revtex, several clarifying comments added

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Cited by in corpus (12)

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• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Mach-Zehnder interferometry of fractional quantum Hall edge states
• Theory of fractional quantum Hall interferometers
• Incompressibility Estimates for the Laughlin Phase
• Anisotropic Quantum Hall Droplets
• Transport of fractional Hall quasiparticles through an antidot
• Piezoelectric coupling, phonons, and tunneling into a quantum Hall edge
• Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime
• Zero Mode Tunnelling in a Fractional Quantum Hall Device
• Edge modes in the fractional quantum Hall effect without extra edge fermions
• The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems