The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a numerical Green function approach, we consider the quantum Hall transition in a microscopic model of non-interacting disordered electrons on a simple square lattice. In a strip geometry, topologically induced edge states extend along the system rim and undergo localization–delocalization transitions as function of energy. We investigate the boundary critical behavior in the lowest Landau band and compare it with a recent tight-binding approach to the bulk critical behavior [Phys. Rev. B 99, 121301(R) (2019)] as well as other recent studies of the quantum Hall transition with both open and periodic boundary conditions.
M. Puschmann et al., "Edge-State Critical Behavior of the Integer Quantum Hall Transition," European Physical Journal: Special Topics, Springer Verlag, Apr 2021.
The definitive version is available at https://doi.org/10.1140/epjs/s11734-021-00064-6
Center for High Performance Computing Research
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07 Apr 2021
This work was supported by the NSF under Grant Nos. DMR-1506152 and DMR-1828489.