Momentum Distribution of the Dilute Fermi Gas

We consider a dilute quantum gas of interacting spin-1/2 fermions in the thermodynamic limit. For a trial state that resolves the ground state energy up to the precision of the Huang–Yang formula, we rigorously derive its momentum distribution. Our result agrees with the formal perturbative argument of Belyakov (Sov. Phys. JETP 13: 850–851 (1961)).