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Solutions exactes de la gravité réduite. Effet Hall quantique de spin

Abstract : The first part is dedicated to the study of gravity in vaccuum when the metric depends only of two variables. Using new Lax pair based on sl(2, R) affine twisted algebra by an order 2 automorphism and Virasoro algebra, we obtain a purely algebraic method (without any integral) to generate all solutions. Metric elements are given by formulae involving determinants. With this new Lax pair, we also study the symplectic structure of the theory. Despite the fact that this model is non ultralocal, we deduce pure c-number Yang Baxter modified equations. We describe how to construct classical observables assuming boundary conditions based on physical hypothesis. The second part deals with the spin quantum Hall effect. We study a generalisation of Chalker-Coddington model, based on a high number of spin degrees of freedom with an Sp(2N) symmetry. We show that there is a direction in coupling constant space, called isotropic direction, preserved by the renormalization flow and attractive in region where coupling constants are positive. We evaluate an effective sigma model for this direction and prove that it corresponds to a massive theory in infrared limit and for large value of N. Finally, the last part is dedicated to a brief survey of density matrix renormalization group algorithm applied to fractional quantum Hall effect. We give some details about basic notions and technics needed for this study. Moreover, we apply some of the numerical tools developped for the DMRG algorithm to find the coupling constants of the Mn12Ac magnetic molecule.
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Contributor : Marc Gingold <>
Submitted on : Thursday, May 23, 2002 - 10:27:36 AM
Last modification on : Tuesday, January 12, 2021 - 7:34:01 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:16:17 PM


  • HAL Id : tel-00001360, version 1



Nicolas Regnault. Solutions exactes de la gravité réduite. Effet Hall quantique de spin. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2002. Français. ⟨tel-00001360⟩



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