Matrix Effective Theories of the Fractional Quantum Hall effect

Abstract

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.

30 pages, 6 figures, to appear in the Al. Zamolodchikov memorial volume

References in corpus (7)

• Physics and Mathematics of Calogero particles
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Correlated tunneling and the instability of the fractional quantum Hall edge
• Hamiltonian Theories of the FQHE
• Incidence of the boundary shape in the effective theory of fractional quantum Hall edges
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory

Cited by in corpus (3)

• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• Noncommutative gauge symmetry in the fractional quantum Hall effect
• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses