Fermi gas with 4-fermion bcs-type interaction

摘要

A gas of spin 1/2 fermions with an interaction V+W = -Σ_κ,κ' gκκ'~bκ~bκ'~b_κ'+Σ_κγκ~bκ~bκ, wher bκ=aκ+aκ- and aκ'σ'κσ satisfy Fermi anticommutation relation, is investigated. The trial ground state |G>is similar in form to the BCS ground state, with b~*_kb~*_k replac- ing a~*_k+a~*_ -k-, but because the excitation energies are not simply additive, the trial density matrix ρ0differs from the BCS one. The expectation values and Tr(H ρ0)are minimized, revealing the presence of a second-order phase transition, with T_c>T_c(BCS)for appropriately adjustedγ_k.