Strong-disorder renormalization group approach to the integer quantum Hall effect

The critical behavior of the integer quantum Hall transition has recently reattracted considerable attention [1]. We propose an alternative numerical approach, namely a modified strong-disorder renormalization group (SDRG) method, in order to investigate this transition. The SDRG method is a recursive decimation process which is known to yield exact results for electronic tight-binding models, provided one keeps all links generated under renormalization. In practical applications, the number of kept links is limited. Nonetheless, in a recent study of the Anderson localization transition, it has been shown that one can get reasonable results for the critical exponents by keeping only a relatively small maximum number of links per site [2]. We generalize this method to the integer quantum Hall problem and apply it to both square lattice and long strip geometries.

[1] PUSCHMANN, M. et al. Integer quantum hall transition on a tight-binding lattice. Phys. Rev. B, American Physical Society, v. 99, p. 121301, 2019.
[2] MARD, H. J. et al. Strong-disorder approach for the anderson localization transition. Phys. Rev. B, American Physical Society, v. 96, p. 045143, 2017.