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Dam Thanh Son (University of Chicago) Les Houches, 09/06/2019

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Dam Thanh Son (University of Chicago) Les Houches, 09/06/2019 Field theory of composite fermions Dam Thanh Son (University of Chicago) Les Houches, 09/06/2019 Part 1: FQHE and field theoretic duality, Dirac composite fermion Part 2: Hydrodynamics of the composite fermions, “emergent graviton” Fractional quantum Hall effect and field-theoretic dualities Plan • Fractional quantum Hall effect • Composite fermion • Duality The quantum Hall effect The microscopic theory of the quantum Hall effect 2D electrons in a magnetic field At the microscopic level: a known Hamiltonian (p + eA )2 e2 H = a a + 2m xa xb a a,b X hXi | − | + impurities Landau levels and IQHE • Ignore interactions between electrons • Energy levels of charged particle in magnetic field in 2D: Landau levels • When some Landau level fully occupied: integer quantum Hall effect (IQHE) von Klitzing et al 1980 Landau levels and IQHE • Ignore interactions between electrons • Energy levels of charged particle in magnetic field in 2D: Landau levels • When some Landau level fully occupied: integer quantum Hall effect (IQHE) von Klitzing et al 1980 n=2 B ∆ = n=1 m BA n=0 degeneracy 2⇡ The fractional quantum Hall effect (FQHE) n=2 n=1 n=0 The fractional quantum Hall effect (FQHE) filling factor number of electrons ⌫ = <latexit 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degeneracy of a LL n=2 n=1 n=0 The fractional quantum Hall effect (FQHE) filling factor number of electrons ⌫ = <latexit 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degeneracy of a LL n=2 n=1 n=0 ⌫<latexit 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< 1 The fractional quantum Hall effect (FQHE) filling factor number of electrons ⌫ = <latexit 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degeneracy of a LL n=2 n=1 n=0 ⌫<latexit 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