Correlation energy of a weakly interacting Fermi gas

• 成果类型: Article
• 署名作者: Benedikter, Niels; Nam, Phan Thanh; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert
• 署名单位: University of Milan; University of Munich; International School for Advanced Studies (SISSA); University of Zurich; Institute of Science & Technology - Austria
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01041-5
• 发表日期: 2021
• 页码: 885-979
• 关键词: gross-pitaevskii equation; hubbard-model; electron-gas; finite-temperature; ward identities; beta-function; 2 dimensions; part i; liquid; bosonization

摘要

We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.