  Site-occupation embedding theory (SOET) [B. Senjean et al., Phys. Rev. B 97,
235105 (2018)] is an in-principle exact embedding method combining wavefunction
theory and density functional theory that gave promising results when applied
to the one-dimensional Hubbard model. Despite its overall good performance,
SOET faces a computational cost problem as its auxiliary impurity-interacting
system remains the size of the full system (which is problematic as the
computational cost increases exponentially with system size). In this work,
this issue is circumvented by employing the Schmidt decomposition, thus leading
to a drastic reduction of the computational cost while retaining the same
accuracy. We show that this projected version of SOET (P-SOET) is competitive
with other embedding techniques such as density matrix embedding theory (DMET)
[G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. In contrast
to the latter, density functional contributions come naturally into play in
P-SOET's framework without any additional computational cost or double counting
effect. As an important result, the density-driven Mott-Hubbard transition
(which is displayed by multiple impurity sites in DMET or in dynamical
mean-field theory) is well described, for the first time, with a single
impurity site.
