By using the Girvin-MacDonald effective Lagrangian for the Hall fluid system at filling nu = 1 we are able to evaluate the ground-state energy for a cylinder of infinite length. That is done by using the topological properties of the edge vacuum in the thermodynamic limit, N-e --> infinity, nu = 1 fixed. From the vacuum energy we extract the value of the Casimir energy for both filling nu = 1 and nu = 1/m. The results obtained fix the central charge c of the underlying 2D Conformal Field Theory at c = 1. This correspondence is further analyzed by using the bosonic realization of the Kac-Moody algebra on the edge vacuum. Then the off-diagonal long-range order of the effective theory can be seen as an equivalent description of the topological order typical of the 2D CFT.

EFFECTIVE LAGRANGIAN, CASIMIR ENERGY AND CONFORMAL FIELD THEORY DESCRIPTION OF THE QUANTUM HALL EFFECT

GIULIANO, Domenico;
1993-01-01

Abstract

By using the Girvin-MacDonald effective Lagrangian for the Hall fluid system at filling nu = 1 we are able to evaluate the ground-state energy for a cylinder of infinite length. That is done by using the topological properties of the edge vacuum in the thermodynamic limit, N-e --> infinity, nu = 1 fixed. From the vacuum energy we extract the value of the Casimir energy for both filling nu = 1 and nu = 1/m. The results obtained fix the central charge c of the underlying 2D Conformal Field Theory at c = 1. This correspondence is further analyzed by using the bosonic realization of the Kac-Moody algebra on the edge vacuum. Then the off-diagonal long-range order of the effective theory can be seen as an equivalent description of the topological order typical of the 2D CFT.
1993
Effective field theories; Quantum Hall Effect; Chern Simons models
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/154819
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