{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/real-space-renormalization-group-approach-to","title":"Real-space renormalization-group approach to the integer quantum Hall effect","arxiv_id":"cond-mat/0501246","date":"2005-01-11","proceeding":null,"authors":["Philipp Cain","Rudolf A. Roemer"],"abstract":"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.","url_abs":"https://arxiv.org/abs/cond-mat/0501246v1","url_pdf":"https://arxiv.org/pdf/cond-mat/0501246v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"real-space-renormalization-group-approach-to","repo_url":"https://github.com/disqs/ccxd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}