Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions
Analysis
This paper investigates the behavior of Hall conductivity in a lattice model of the Integer Quantum Hall Effect (IQHE) near a localization-delocalization transition. The key finding is that the conductivity exhibits heavy-tailed fluctuations, meaning the variance is divergent. This suggests a breakdown of self-averaging in transport within small, coherent samples near criticality, aligning with findings from random matrix models. The research contributes to understanding transport phenomena in disordered systems and the breakdown of standard statistical assumptions near critical points.
Key Takeaways
- •The study focuses on Hall conductivity fluctuations in the IQHE.
- •Heavy-tailed fluctuations are observed near the localization-delocalization transition.
- •The findings suggest a breakdown of self-averaging in transport.
- •Results are consistent with random matrix models.
“The conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance.”