Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
arXiv:1411.3105 · doi:10.1016/j.aop.2015.02.013
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.
v1: 60+21 pages; v2: 63 pages, 8 appendices, minor changes to improve clarity and format, fix typos, and expand references; v3: 65 pages, 8 appendices, revised and expanded discussions in the introduction and sections 9-11, major revisions to appendix E, minor changes in notation to improve clarity, and further expanded references
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