Conserving and gapless approximations for the composite bosons in terms of the constituent fermions

Abstract

A long-standing problem with the many-body approximations for interacting condensed bosons has been the dichotomy between the ``conserving'' and ``gapless'' approximations, which either obey the conservations laws or satisfy the Hugenholtz-Pines condition for a gapless excitation spectrum, in the order. It is here shown that such a dichotomy does not exist for a system of composite bosons, which form as bound-fermion pairs in the strong-coupling limit of the fermionic attraction. By starting from the constituent fermions, for which conserving approximations can be constructed for any value of the mutual attraction according to the Baym-Kadanoff prescriptions, it is shown that these approximations also result in a gapless excitation spectrum for the boson-like propagators in the broken-symmetry phase. This holds provided the corresponding equations for the fermionic single- and two-particle Green's functions are solved self-consistently.

arXiv comment4 pages, 1 figure

References in corpus (6)

• Observation of Bose-Einstein Condensation of Molecules
• Creation of ultracold molecules from a Fermi gas of atoms
• Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
• Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas
• Spectroscopic insensitivity to cold collisions in a two-state mixture of fermions
• Renormalization group flows into phases with broken symmetry

Cited by in corpus (3)

• Thermodynamics of the BCS-BEC crossover
• Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase