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Application of the operator product expansion and sum rules to the study of the single-particle spectral density of the unitary Fermi gas
The unitary Fermi gas consists of two species of non-relativistic fermions with equal mass. It has been studied intensively during the last decade and has attracted much interest partly because of its experimental realization in ultracold atomic gases. In the work to be presented in this seminar, we have developed a novel method for studying this system, which makes use of the operator product expansion to derive a general class of sum rules on the imaginary part of the single-particle self-energy. These sum rules are furthermore analyzed by the maximum entropy method, which allows us to obtain the single-particle spectral density as a function of both energy and momentum. The spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.