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arXiv · 1805.09958

Integer quantum Hall transition on a tight-binding lattice

Martin Puschmann·Philipp Cain·Michael Schreiber·Thomas Vojta
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Abstract

Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ significantly from each other, casting doubt on our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [Phys. Rev. B 95, 125414 (2017)] recently suggested that the semiclassical Chalker-Coddington model, widely employed in numerical simulations, is incomplete, questioning the established central theoretical results. To shed light on the controversy, we perform a high-accuracy study of the integer quantum Hall transition for a microscopic model of disordered electrons. We find a localization length exponent $\nu=2.58(3)$ validating the result of the Chalker-Coddington network.

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Martin Puschmann, Philipp Cain, Michael Schreiber, Thomas Vojta. 2018-05-25. Integer quantum Hall transition on a tight-binding lattice. https://doi.org/10.1103/physrevb.99.121301

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