Thermal resonating Hartree–Bogoliubov theory based on the projection method

Abstract

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–Bogoliubov (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 〉(N: Number of single-particle states) is expressed as Tr (e-βH) = 2N-1∫〈g|e-βH|g〉dg (β = 1/kBT). Introducing a projection operator P to the Res-HB subspace, the PF in the Res-HB subspace is given as Tr (Pe-βH), which is calculated within the Res-HB subspace by using the Laplace transform of e-βH 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.