  In quantum droplets, the mean-field energy is comparable to the
Lee-Huang-Yang (LHY) energy. In the Bogoliubov theory, the LHY energy of the
quantum droplet has an imaginary part, but it is neglected for practical
purposes. So far, most theoretical studies of quantum droplets have been based
on the extended Gross-Pitaevskii (GP) equation obtained by adding the LHY
energy to the GP equation. In this article, we present the density-functional
theory of quantum droplets. In our approach, the quantum fluctuations in
quantum droplets, as described by an effective action, generate the correlation
energy which is real and can be determined self-consistently. Using the
density-functional theory, we calculate higher-order corrections to the energy,
the quantum depletion fraction, and the excitations of the droplet. Our results
for the ground-state energy and the quantum depletion fraction are compared
with the Monte Carlo results and good agreement is found. The implications of
our theory are discussed.
