Localization-length exponent in two models of quantum Hall plateau transitions

Abstract

Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-thanexpected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the exponent calculation in the continuum model and in the lattice model, both projected to the lowest Landau level or subband. Combining scaling results with or without the corrections of an irrelevant length scale, we obtain ν = 2.48 ± 0.02, which is larger but still consistent with the earlier results in the two models, unlike what was found recently in the network model. The scaling of the total number of conducting states, as determined by the Chern number calculation, is accompanied by an effective irrelevant length scale exponent y = 4.3 in the lattice model, indicating that the irrelevant perturbations are insignificant in the topology number calculation.

Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition

“…The integer quantum Hall transition (IQHT) at E ¼ E c is the most studied Anderson transition [2] because of its conceptual simplicity, low dimensionality, and experimental relevance. However, critical properties at the IQHT are notoriously difficult to compute analytically; they are mostly known from numerical studies which employed the Chalker-Coddington (CC) network model [3][4][5][6][7][8][9][10][11][12][13], microscopic continuous [14,15], lattice [10,[14][15][16][17], and Floquet Hamiltonians [18]. In recent works, the critical properties agree among models, indicating universality of the IQHT.…”

Composite fermion nonlinear sigma models

“…Because the set of delocalized states is of measure zero, interactions must be included for nonzero finite-temperature longitudinal conductivity [7]. The numerically calculated localization length critical exponent ν calc (varying from about 2.48-2.62 with the specific lattice model and calculation details [8][9][10][11][12][13][14][15][16]) do not appear to lie within the error bars of the measured exponent ν ≈ 2.38 [17,18]. (Some recent works are critical of these theoretical results: inclusion of additional types of disorder may be relevant [19] and/or the critical scaling regime may require significantly larger systems sizes [20]; see also [21,22].)…”

Topology and many-body localization

“…We now recognize this as being due to the topological nature [14,15] of Landau levels, which have given rise to a much richer set [16] of universality classes of disordered systems, beyond the original Wigner-Dyson classes [4]. This divergence has been much studied by diverse numerical methods [17,18,19,20], though the precise critical exponent [21,22,23], and even the nature [24,25] of the divergence is still being debated.…”