Matrix E ffective Theories of the Fractional Quantum Hall eff ect

Cappelli, Andrea and Rodriguez, Ivan D. (2009) Matrix E ffective Theories of the Fractional Quantum Hall eff ect. Journal of Physics A: Mathematical and Theoretical, 42 (304006). pp. 1-30. ISSN 1751-8121

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The present understanding of nonperturbative ground states in the fractional quantum Hall e ffect is based on eff ective theories of the Jain \composite fermion" excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum Hall eff ect, where the composite-fermion construction naturally follows from gauge invariance. The matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the Laughlin and Jain hierarchical states. The matrix theory possesses a physical limit for commuting matrices that could be reachable while staying in the same phase.

Item Type: Article
Additional Information: Preprint version of original article © 2009 IOP Publishing Ltd. The authors would like to thank the hospitality of the G. Galilei Institute for Theoretical Physics, Florence. This work was partially funded by the ESF programme INSTANS: Interdisciplinary Statistical and Field Theory Approaches to Nanophysics and Low Dimensional Systems, and by the MUR grant Fisica Statistica dei Sistemi Fortemente Correlati all'Equilibrio e Fuori dall'Equilibrio.
Keywords: Matrix E ffective Theories; Fractional Quantum Hall eff ect; matrix gauge theory;
Academic Unit: Faculty of Science and Engineering > Mathematical Physics
Item ID: 2700
Identification Number: doi: 10.1088/1751-8113/42/30/304006
Depositing User: Dr. Ivan Rodriguez
Date Deposited: 09 Sep 2011 11:59
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: Institute of Physics Publishing Ltd
Refereed: No

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