3 research outputs found
NC Effective Gauge Model for Multilayer FQH States
We develop an effective field model for describing FQH states with rational
filling factors that are not of Laughlin type. These kinds of systems, which
concern single layer hierarchical states and multilayer ones, were observed
experimentally; but have not yet a satisfactory non commutative effective field
description like in the case of Susskind model. Using brane analysis and
fiber bundle techniques, we first classify such states in terms of
representations characterized, amongst others, by the filling factor of the
layers; but also by proper subgroups of the underlying gauge symmetry.
Multilayer states in the lowest Landau level are interpreted in terms of
systems of branes; but hierarchical ones are realized as Fiber bundles on
which we construct explicitly. In this picture, Jain and Haldane series
are recovered as special cases and have a remarkable interpretation in terms of
Fiber bundles with specific intersection matrices. We also derive the general
NC commutative effective field and matrix models for FQH states, extending
Susskind theory, and give the general expression of the rational filling
factors as well as their non abelian gauge symmetries.Comment: 54 pages 11 figures, LaTe