Self-consistent description of Bose-Bose droplets: modified gapless Hartree-Fock-Bogoliubov method

We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the generalized Gross-Pitaevskii equation accounting for quantum depletion and renormalized anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations. We derive well defined procedure to calculate the zero temperature renormalized anomalous density-the quantity needed to correctly describe the formation of quantum liquid droplet. We pay particular attention to the case of droplets harmonically confined in some directions. The method allows to determine the Lee-Huang-Yang-type contribution to the chemical potential of inhomogeneous droplets when the local density approximation fails.

Automated summary

The article presents a formal description of the ground state of a weakly interacting Bose system, taking into account higher order terms in the energy expansion. This approach is applicable to a Bose-Bose mixture in a weak collapse regime where quantum fluctuations stabilize the system and lead to the formation of quantum liquid droplets. By using the generalized Gross-Pitaevskii equation and modified Bogoliubov equations, a self-consistent calculation of the renormalized anomalous density at zero temperature is derived, which is essential for accurately describing the formation of quantum liquid droplets.