{"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/robust-analytic-continuation-using-sparse","title":"Robust analytic continuation using sparse modeling approach imposed by semi-positive definiteness for multi-orbital systems","arxiv_id":"2409.01509","date":"2024-09-03","proceeding":null,"authors":["Yuichi Motoyama","Hiroshi Shinaoka","Junya Otsuki","Kazuyoshi Yoshimi"],"abstract":"Analytic continuation (AC) from imaginary-time Green's function to spectral function is essential in the numerical analysis of dynamical properties in quantum many-body systems. However, this process faces a fundamental challenge: it is an ill-posed problem, leading to unstable spectra against the noise in the Green's function. This instability is further complicated in multi-orbital systems with hybridization between spin-orbitals, where off-diagonal Green's functions yield a spectral matrix with off-diagonal elements, necessitating the matrix's semi-positive definiteness to satisfy the causality. We propose an advanced AC method using sparse modeling for multi-orbital systems, which reduces the effect of noise and ensures the matrix's semi-positive definiteness. We demonstrate the effectiveness of this approach by contrasting it with the conventional sparse modeling method, focusing on handling Green's functions with off-diagonal elements, thereby demonstrating our proposed method's enhanced stability and precision.","url_abs":"https://arxiv.org/abs/2409.01509v1","url_pdf":"https://arxiv.org/pdf/2409.01509v1.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":"robust-analytic-continuation-using-sparse","repo_url":"https://github.com/SpM-lab/pySpMAC","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"robust-analytic-continuation-using-sparse","repo_url":"https://isspns-gitlab.issp.u-tokyo.ac.jp/y-motoyama/spmac_multi","is_official":1,"mentioned_in_paper":0,"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}