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Making use of the operator product expansion, we derive a general class ofsum rules for the imaginary part of the single-particle self-energy of theunitary Fermi gas. The sum rules are analyzed numerically with the help of themaximum entropy method, which allows us to extract the single-particle spectraldensity as a function of both energy and momentum. These spectral densitiescontain basic information on the properties of the unitary Fermi gas, such asthe dispersion relation and the superfluid pairing gap, for which we obtainreasonable agreement with the available results based on quantum Monte-Carlosimulations.

annals of physics

Single-particle spectral density of the unitary Fermi gas: Novel  approach based on the operator product expansion, sum rules and the maximum  entropy method