Geometry of quantum Hall states: Gravitational anomaly and transport coefficients |
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Authors: | Tankut Can Michael Laskin Paul B Wiegmann |
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Institution: | 1. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY 11794, USA;2. Department of Physics, University of Chicago, 929 57th St, Chicago, IL 60637, USA |
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Abstract: | We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism. |
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Keywords: | Quantum Hall effect Kä hler geometry Laughlin wave function |
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