Cappelli, Andrea and Rodriguez, Ivan D.
Matrix Effective Theories of the Fractional
Quantum Hall effect.
Journal of Physics A: Mathematical and Theoretical, 42 (304006).
The present understanding of nonperturbative ground states in the
fractional quantum Hall effect is based on effective 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 effect, 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.
||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.
||Matrix Effective Theories; Fractional
Quantum Hall effect; matrix gauge theory;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Ivan Rodriguez
||09 Sep 2011 11:59
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||Journal of Physics A: Mathematical and Theoretical
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