{"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/toolkit-for-general-2d-scalar-potential-in","title":"Toolkit for General 2d Scalar Potential in LCT","arxiv_id":"2412.12255","date":"2024-12-16","proceeding":null,"authors":["A. Liam Fitzpatrick","Emanuel Katz","Yuan Xin"],"abstract":"We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in $1+1d$, and find precise agreement with integrability results when the scaling dimension $\\Delta$ of the deforming cosine/cosinh potential is in the range $ \\Delta \\leq 1$. The agreement provides additional evidence for a recent conjecture for how to compute the effective lightcone Hamiltonian in this class of models. In addition, to high precision, we provide the first direct confirmation for the conjectured self-duality of the sinh-Gordon model ($\\Delta < 0)$, which relates $\\Delta \\leftrightarrow 4/\\Delta$. As the dimension approaches the upper limit $\\Delta=1$ from below, we show analytically that the Hamiltonian matrix elements exactly reproduce those of a free Majorana fermion, demonstrating how bosonization is manifested in the LCT basis. We comment on the possible extension of the approach to $\\Delta > 1$.","url_abs":"https://arxiv.org/abs/2412.12255v3","url_pdf":"https://arxiv.org/pdf/2412.12255v3.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":"toolkit-for-general-2d-scalar-potential-in","repo_url":"https://github.com/andrewliamfitz/lct","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}