Spectral Properties of Three Dimensional Layered Quantum Hall Systems

Abstract

We investigate the spectral statistics of a network model for a three dimensional layered quantum Hall system numerically. The scaling of the quantity $J_0=1/2<s^2>$ is used to determine the critical exponent $\nu$ for several interlayer coupling strengths. Furthermore, we determine the level spacing distribution $P(s)$ as well as the spectral compressibility $\chi$ at criticality. We show that the tail of $P(s)$ decays as $\exp (-\kappa s)$ with $\kappa =1/(2\chi )$ and also numerically verify the equation $\chi =(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the spatial dimension.

4 pages, 5 figures submitted to J. Phys. Soc. Jpn

References in corpus (5)

• The Anderson transition: time reversal symmetry and universality
• Boundary conditions at the mobility edge
• Anomalous diffusion at the Anderson transitions
• Localization and Metal-Insulator Transition in Multi-Layer Quantum Hall Structures
• Spectral Properties of the Chalker-Coddington Network

Cited by in corpus (4)

• Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
• Renormalization group approach to energy level statistics at the integer quantum Hall transition
• Modeling Disordered Quantum Systems with Dynamical Networks
• Real-space renormalization-group approach to the integer quantum Hall effect