Abstract
We apply the real-space renormalization group (RG) approach to investigate the energy level statistics at the integer quantum Hall (QH) transition. Within the RG approach the macroscopic array of saddle points of the Chalker–Coddington network is replaced by a fragment consisting of only five saddle points. Previously, we have demonstrated that the RG approach reproduces the distribution of the conductance at the transition, P( G), with very high accuracy. To assess the level statistics we analyze the phases of the transmission coefficients of the saddle points. We find that, at the transition, the nearest-neighbor energy level spacing distribution (LSD) exhibits well-pronounced level repulsion. We emphasize that a metal-like LSD emerges when the fixed point distribution P c of G is used. Studying the change of the LSD around the QH transition we observe scaling behavior. Using a one-parameter finite-size scaling analysis we are able to extract a critical exponent ν=2.38±0.04 of the localization length.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physica E: Low-dimensional Systems and Nanostructures
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.