International Journal of Modern Physics B

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

Gerardo Cristofano, Domenico Giuliano, G. Maiella

Published Aug 30, 1994• 3 citations

Abstract

By using the Girvin–MacDonald effective Lagrangian for the Hall fluid system at filling ν = 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, Ne → ∞, ν = 1 fixed, From the vacuum energy we extract the value of the Casimir energy for both filling ν = 1 and ν = 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.

DOI: 10.1142/s0217979294001068

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