{"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/two-dimensional-bose-hubbard-model-for-helium","title":"Two-Dimensional Bose-Hubbard Model for Helium on Graphene","arxiv_id":"2102.11288","date":"2021-02-22","proceeding":null,"authors":["Jiangyong Yu","Ethan Lauricella","Mohamed Elsayed","Kenneth Shepherd Jr.","Nathan S. Nichols","Todd Lombardi","Sang Wook Kim","Carlos Wexler","Juan M. Vanegas","Taras Lakoba","Valeri N. Kotov","Adrian Del Maestro"],"abstract":"An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(U\\approx\\infty)$, repulsive nearest-neighbor $(V>0)$ and small attractive $(V'<0)$ next-nearest neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively point-like, the detailed microscopic form of the short range electrostatic and long range dispersion interactions in the helium-graphene system are crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of $^4$He adsorbed on graphene deep in the commensurate solid phase with $1/3$ of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.","url_abs":"https://arxiv.org/abs/2102.11288v2","url_pdf":"https://arxiv.org/pdf/2102.11288v2.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":"two-dimensional-bose-hubbard-model-for-helium","repo_url":"https://github.com/DelMaestroGroup/papers-code-BoseHubbardModelHeAdsorptionGraphene","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"two-dimensional-bose-hubbard-model-for-helium","repo_url":"https://github.com/yuj120254/BHHeGraphene","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}