Journal
ANNALS OF PHYSICS
Volume 362, Issue -, Pages 752-794Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2015.02.013
Keywords
Quantum Hall effect; Kahler geometry; Laughlin wave function
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Funding
- National Science Foundation Grants [DMS-1206648, DMS-1156656, DMR-MRSEC-1420709]
- CNPq-Brazil Science Without Borders Program
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206648] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1156636] Funding Source: National Science Foundation
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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. (C) 2015 Published by Elsevier Inc.
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