{"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/time-translation-invariance-symmetry-breaking","title":"Time-translation invariance symmetry breaking hidden by finite-scale singularities","arxiv_id":"2412.11619","date":"2024-12-16","proceeding":null,"authors":["Ixandra Achitouv","Vincent Lahoche","Dine Ousmane Samary","Parham Radpay"],"abstract":"In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean $\\mathbb{R}^N$ space through the complex landscape provided by a disordered Hamiltonian of type $2+p$. We focus on the large $N$ limit, where the coarse-graining procedure is unconventional: it is based on the Wigner spectrum of the rank-2 disorder. The main consequence of this choice is that canonical dimensions depend on the scale, and the flow equations fail to become autonomous, preventing the existence of global fixed points. One of the main features of the underlying renormalization group flow is the existence of finite-scale singularities for initial conditions sufficiently close to the Gaussian region and for rank-$p$ disorder intensity large enough. Using the Luttinger-Ward formalism, we show that these finite-scale singularities hide (and should be resolved by) a phase transition that breaks time-translation invariance.","url_abs":"https://arxiv.org/abs/2412.11619v2","url_pdf":"https://arxiv.org/pdf/2412.11619v2.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":"time-translation-invariance-symmetry-breaking","repo_url":"https://github.com/ixandraachitouv/timetransinvsymbreakhidden","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}