Poster Grande
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Tunneling exponents from non-commutative Chern-Simons theory D.C. Cabra1,2 N.E. Grandi3,4 1
Laboratoire de Physique Theorique, Universite Louis Pasteur, 3 rue de l’Universite, F-67084 Strasbourg Cedex, France 2 Facultad de Ingenieria, UNLZ, Cno. de Cintura y Juan XXIII, (1832) Lomas de Zamora, Argentina 3 IFLP - Dto. de Fisica UNLP, C.C. 67, (1900) La Plata, Argentina 4 SISSA, Via Beirut 4, 34014 Trieste, Italy)
We construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. We include higher order corrections to the low energy theory, following a hydrodynamical derivation (which led to a non-commutative version of the ChernSimons action) modified so as to admit a boundary. The effective theory obtained is the standard chiral boson theory, with an additional self-interacting term which is induced by the boundary. It turns out that the tunnelling exponent receives a correction which is negative and does not depend on the filling fraction, though it is non-universal. This is in qualitative agreement with experiments, that systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.
The action is projected into the lowest Landau Level by dropping the kinetic term.
The electric field is linearized in the neighborhood of each particle, and then eliminated by a boost
The resulting theory is invariant under area preserving diffeomorfisms
The resulting constraint is solved in terms of a scalar field
After a continuum limit the system is boosted back to the rest frame.
The final action is not a boundary action, even if their degrees of freedom localize at the inhomogeneities of the sample The resulting exponent is smaller than the standard result, in qualitative agreement with experiments.
This is re-discretized in the y direction, cutting the edge in N slices of width ∆y N
N=1
In the case of a single slice, we get a self interacting chiral boson
After a one loop calculation we get the correction in the propagator, and then in the tunneling exponent.
The resulting exponent is smaller than the standard result, in qualitative agreement with experiments.
Laboratoire de Physique Theorique, Universite Louis Pasteur, 3 rue de l’Universite, F-67084 Strasbourg Cedex, France 2 Facultad de Ingenieria, UNLZ, Cno. de Cintura y Juan XXIII, (1832) Lomas de Zamora, Argentina 3 IFLP - Dto. de Fisica UNLP, C.C. 67, (1900) La Plata, Argentina 4 SISSA, Via Beirut 4, 34014 Trieste, Italy)
We construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. We include higher order corrections to the low energy theory, following a hydrodynamical derivation (which led to a non-commutative version of the ChernSimons action) modified so as to admit a boundary. The effective theory obtained is the standard chiral boson theory, with an additional self-interacting term which is induced by the boundary. It turns out that the tunnelling exponent receives a correction which is negative and does not depend on the filling fraction, though it is non-universal. This is in qualitative agreement with experiments, that systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.
The action is projected into the lowest Landau Level by dropping the kinetic term.
The electric field is linearized in the neighborhood of each particle, and then eliminated by a boost
The resulting theory is invariant under area preserving diffeomorfisms
The resulting constraint is solved in terms of a scalar field
After a continuum limit the system is boosted back to the rest frame.
The final action is not a boundary action, even if their degrees of freedom localize at the inhomogeneities of the sample The resulting exponent is smaller than the standard result, in qualitative agreement with experiments.
This is re-discretized in the y direction, cutting the edge in N slices of width ∆y N
N=1
In the case of a single slice, we get a self interacting chiral boson
After a one loop calculation we get the correction in the propagator, and then in the tunneling exponent.
The resulting exponent is smaller than the standard result, in qualitative agreement with experiments.
