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

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.
Effective field theories; Quantum Hall Effect; Chern Simons models
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/154819
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 2
social impact