Critical behavior at the integer quantum Hall transition in a network model on the kagome lattice

Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition

“…Their result, ν = 2.593 [2.578, 2.598] (where the numbers in brackets mark the confidence interval), was clearly higher than what was observed in earlier numerical investigations as well as experiments. In the following years, several other investigations confirmed this new, larger value of ν [9][10][11][12] but more recently, the reported results have been more diverse. A value of ν = 2.37 (2) (where the number in brackets gives the error of the last digit) was obtained for a structurally disordered CC network [13,14].…”

“…Note that the constant b defines a characteristic length L 0 = exp(−b) ≈ 0.53 (in multiples of the renormalized lattice constant). If we add an additional power-law term with exponent y , the L-range for good fits increases to L ≥ 8, and we find Γ c = 0.742(4) and b = 0.28 (11) with y = 0.96 (15).…”

Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions

“…Taking inspiration from this semi-classical picture, J. Chalker and P. Coddington (CC) [3] formulated a network model of quantum scattering nodes based on a regular lattice that is meant to provide an effective description of the physics of edge states (the only relevant degrees of freedom in plateau transitions). Its generalization on a Kagome lattice was proposed in [4] and a similar network model for the Spin Quantum Hall Effect (SQHE) was studied in [5,6]. Numerical investigations of the localization length ξ at the critical point, i.e.…”

“…Numerical investigations of the localization length ξ at the critical point, i.e. ξ ∼ (t − t c ) −ν with t c = 1/ √ 2, resulted in ν = 2.56 ± 0.62 for a regular lattice [7-9, 11, 12] and ν = 2.658 ± 0.046 for the Kagome lattice [4]. Both these values are not compatible with the experimental value ν = 2.38 ± 0.06 measured for plateau transitions in the IQHE [13,14].…”