{"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/conformal-invariance-and-multifractality-at","title":"Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions","arxiv_id":"2306.07340","date":"2023-06-12","proceeding":null,"authors":["Jaychandran Padayasi","Ilya A. Gruzberg"],"abstract":"Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators $O_q$ with scaling dimensions $\\Delta_q$ in a field-theory description of the transitions. The operators $O_q$ satisfy the so-called Abelian fusion expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum $\\Delta_q$ (and its generalized form) must be quadratic in its arguments in any dimension $d \\geq 2$.","url_abs":"https://arxiv.org/abs/2306.07340v2","url_pdf":"https://arxiv.org/pdf/2306.07340v2.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":"conformal-invariance-and-multifractality-at","repo_url":"https://github.com/jaychandran-padayasi/coulomb-gas-expansion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}