Exploring the Global Phase Diagram of Quantum Hall Systems

Frédéric Chandelier, Y. Georgelin, Thierry Masson +1 more

D. N. Sheng, Leon Balents, Ziqiang Wang

L. W. Wong

Akira Fukuda, A. Sawada, K. IWATA +6 more

C.A. Lütken

It is suggested that it is not necessary to solve the full non-perturbative problem of two-dimensional charge transport in order to obtain global information about the phase and flow diagrams for the quantum Hall system and its relatives. It is argued that the effective quantum field theories encoding the macroscopic properties of these systems are invariant under a symmetry contained in the modular group. New phase and flow diagrams are obtained which exhibit a hierarchy of only odd or only even phases (Hall plateaus). The Kramers-Wannier-like symmetry determines the exact location of all renormalization group fixed points, which appear to be in agreement with available scaling experiments on the quantum Hall system. It also explains the observed 'super-universality', of the delocalization exponent.

David Carpentier

Using the renormalization group (RG) we study two-dimensional electromagnetic Coulomb gas and extended sine-Gordon theories invariant under the modular group SL (2, ). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following the proposal for a SL (2, ) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.