Real-space renormalization-group approach to the integer quantum Hall effect
| dc.creator | Cain, Philipp | |
| dc.creator | Roemer, Rudolf A. | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T03:03:10Z | |
| dc.date.available | 2026-07-07T03:03:10Z | |
| dc.description | We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G) yields a value of the critical exponent nu that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as R_L and R_H is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD) which is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with nu=2.37\pm 0.02. Away from the transition it changes towards the Poisson distribution. We next investigate the plateau-to-insulator transition. For a fully quantum coherent situation, we find a quantized Hall insulator with R_H ~ h/e^2 up to R_L ~ 20 h/e^2 when interpreting the results in terms of the most probable value of the distribution P(R_H). Upon further increasing R_L, the Hall insulator with diverging R_H ~ R_L^kappa is seen. This crossover depends on the precise nature of the averaging of P(R_L) and P(R_H). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition modeled by a power law correlation in the random potential. Similar to the classical percolation, we observe an enhancement of nu with decreasing correlation range. These results exemplify the surprising fact that a small RG unit, containing five nodes, accurately captures most of the correlations responsible for the QH transition. | |
| dc.description | 35 pages, 14 figures, submitted to Int. J. Mod. Phys. B | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0501246 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0501246 | |
| dc.identifier | Int. J. Mod. Phys. B 19, 2085-2119 (2005) | |
| dc.identifier | doi:10.1142/S0217979205029742 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/25655 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.title | Real-space renormalization-group approach to the integer quantum Hall effect | |
| dc.type | text |