{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,20]],"date-time":"2024-04-20T08:25:27Z","timestamp":1713601527692},"reference-count":65,"publisher":"World Scientific Pub Co Pte Lt","issue":"20","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Mod. Phys. B"],"published-print":{"date-parts":[[2014,8,10]]},"abstract":"<jats:p> We propose a rigorous thermal resonating mean-field theory (Res-MFT). A state is approximated by superposition of multiple MF wavefunctions (WFs) composed of non-orthogonal Hartree\u2013Bogoliubov (HB) WFs. We adopt a Res-HB subspace spanned by Res-HB ground and excited states. A partition function (PF) in a SO (2N) coherent state representation (CS Reps) |g \u3009(N: Number of single-particle states) is expressed as Tr (e<jats:sup>-\u03b2H<\/jats:sup>) = 2<jats:sup>N-1<\/jats:sup>\u222b\u3008g|e<jats:sup>-\u03b2H<\/jats:sup>|g\u3009dg (\u03b2 = 1\/k<jats:sub>B<\/jats:sub>T). Introducing a projection operator P to the Res-HB subspace, the PF in the Res-HB subspace is given as Tr (Pe<jats:sup>-\u03b2H<\/jats:sup>), which is calculated within the Res-HB subspace by using the Laplace transform of e<jats:sup>-\u03b2H<\/jats:sup> and the projection method. The variation of the Res-HB free energy is made, which leads to a thermal HB density matrix [Formula: see text] expressed in terms of a thermal Res-FB operator [Formula: see text] as [Formula: see text]. A calculation of the PF by an infinite matrix continued fraction (IMCF) is cumbersome and a procedure of tractable optimization is too complicated. Instead, we seek for another possible and more practical way of computing the PF and the Res-HB free energy within the Res-MFT. <\/jats:p>","DOI":"10.1142\/s0217979214501318","type":"journal-article","created":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T08:08:06Z","timestamp":1401437286000},"page":"1450131","source":"Crossref","is-referenced-by-count":1,"title":["Thermal resonating Hartree\u2013Bogoliubov theory based on the projection method"],"prefix":"10.1142","volume":"28","author":[{"given":"Seiya","family":"Nishiyama","sequence":"first","affiliation":[{"name":"Centro de F\u00edsica Computacional, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"Jo\u00e3o","family":"da Provid\u00eancia","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica Computacional, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"Hiromasa","family":"Ohnishi","sequence":"additional","affiliation":[{"name":"Department of General Science, Tsuruoka National College of Technology, 104 Sawada, Inooka, Tsuruoka, Yamagata, 997-8511, Japan"}]}],"member":"219","published-online":{"date-parts":[[2014,6,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/2262"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.69.2863"},{"key":"rf3","first-page":"865","volume":"31","author":"Dagotto E.","journal-title":"Phys. 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