{"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/gauge-fixing-canonical-forms-and-optimal","title":"Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops","arxiv_id":"1801.05390","date":"2018-01-16","proceeding":null,"authors":["Glen Evenbly"],"abstract":"We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal correlations present in a tensor network is proposed, which quantifies the extent of resonances around closed loops in the network. Finally we describe an algorithm for the optimal truncation of an internal index from a tensor network, based upon proper removal of the redundant internal correlations. These results, which offer a unified theoretical framework for the manipulation of tensor networks with closed loops, can be applied to improve existing tensor network methods for the study of many-body systems and may also constitute key algorithmic components of sophisticated new tensor methods.","url_abs":"http://arxiv.org/abs/1801.05390v2","url_pdf":"http://arxiv.org/pdf/1801.05390v2.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":"gauge-fixing-canonical-forms-and-optimal","repo_url":"https://github.com/brucelyu/tensorRGflow","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","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}