Scaling, Diffusion, and the Integer Quantized Hall Effect

Abstract

The behavior of the two-particle spectral function, S(q,co), is examined in the hydrodynamic regime, at the mobility edge in a model for the integer quantized Hall effect. Results are presented from numerical diagonalization of the Hamiltonian for finite systems. For q 2 /co small, S(q,co) has a conventional, diffusive form. For q 2 /co large, the novel dependence Siq.^ -co'^q ~2 +TJ is obtained, with 77^0.38 ± 0.04.

Quantum Hall effect at finite temperatures

“…20 For non-interacting electrons D 2 = 2−η, where η ≃ 0.4 is the critical exponent of eigenfunction correlations. 8 The problem is more delicate in the interactiondominated regime (T ≪ T c ); within the framework of the above approach, however, the fractal dimension D 2 in Eq. (6) is just half that for non-interacting electrons.…”

Correlated quantum percolation in the lowest Landau level

“…In most studies of localization, the Green's function is calculated in the momentum-frequency domain and studied in detail in the limit of large momenta/small frequency 2,22 . The purpose of this section is to show explicitly how the critical exponent ν q can be extracted from the Green's function using instead the real time domain, as proposed by Sinova, Meden and Girvin 23 .…”

Integer quantum Hall effect in double-layer systems

“…(4.7), allows us to rewrite the finite-size scaling relation, Eq. (4.5), in the following form, 8) which is the form we shall use in the analysis of the numerical results.…”