Luttinger theorem and imbalanced Fermi systems

Abstract

The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "$\Phi$-derivable" approximation, and illustrate it in particular for the self-consistent $t$-matrix approximation.

6 pages, 2 figures

References in corpus (7)

• Thermodynamics of the BCS-BEC crossover
• Normal state of highly polarized Fermi gases: Full many-body treatment
• Evolution of the Normal State of a Strongly Interacting Fermi Gas from a Pseudogap Phase to a Molecular Bose Gas
• BCS-BEC crossover in an asymmetric two-component Fermi gas
• Non-perturbative conserving approximations and Luttinger's sum rule
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Cited by in corpus (6)

• The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review
• Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
• Evolution of an attractive polarized Fermi gas: From a Fermi liquid of polarons to a non-Fermi liquid at the Fulde-Ferrell-Larkin-Ovchinnikov quantum critical point
• Application of renormalized RPA to polarized Fermi gases
• Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures
• Number conservation in odd-particle number random phase approximation and extensions