Tan's contact as an indicator of completeness and self-consistency of a theory
Abstract
It is well known that Tan's contact could be calculated by using any of the following three methods: by the asymptotic behavior of momentum distribution, by Tan's adiabatic sweep theorem, or by the operator product expansion as an expectation value of the interaction term. We argue that if a theory describing a Bose (or Fermi) system with the only contact interaction is self-consistent, then it should lead to the same result in all three cases. As an example, we considered mean-field theory (MFT)-based approaches and established that among existing approximations of MFT, the Hartree-Fock-Bogoliubov (HFB) approach is the most self-consistent. Actually, HFB is able to describe existing experimental data on Tan's contact for dilute Bose gas but fails to predict its expected behavior at large gas parameters $(\ensuremath{\gamma}>0.015)$. So, for appropriate description of properties of a Bose gas even at zero temperature, this approximation needs to be expanded by taking into account fluctuations in higher order then the second one.