The geometry of the fractional quantum Hall effect: Exposing the gravitational anomaly /

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Bibliographic Details
Author / Creator:Laskin, Michael, author.
Ann Arbor : ProQuest Dissertations & Theses, 2016
Description:1 electronic resource (86 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Hidden Bibliographic Details
Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Paul Wiegmann Committee members: William Irvine; Michael Levin; Dam Thanh Son.
Dissertation Abstracts International, Volume: 78-06(E), Section: B.
Summary:We study quantum Hall states on curved surfaces with the aim of exposing the gravitational anomaly. We develop two general methods for computing correlation functions of the fractional quantum Hall effect (FQHE) on curved surfaces - the Ward Identity and Field Theory. We then show that on surfaces with conical singularities, the electronic fluid near the tip of the cone has an intrinsic angular momentum due solely to the gravitational anomaly. This is effect occurs because quantum Hall states behave as conformal primaries near singular points, with a conformal dimension equal to the angular momentum. We argue that the gravitational anomaly and conformal dimension determine the fine structure of the electronic density at the conical point. The singularities emerge as quasi-particles with spin and exchange statistics arising from adiabatically braiding conical singularities. Thus, the gravitational anomaly, which appears as a finite size correction on smooth surfaces, dominates geometric transport on singular surfaces.