  Efficient and accurate computational methods for dealing with interacting
electron problems on a lattice are of broad interest to the condensed matter
community. For interacting Hubbard models, we introduce a cluster
slave-particle approach that provides significant computational savings with
high accuracy for total energies, site occupancies, and interaction energies.
Compared to exact benchmarks using density matrix renormalization group for
$d$-$p$ Hubbard models, our approach delivers accurate results using two to
three orders of magnitude lower computational cost. Our method is based on a
novel slave-particle decomposition with an improved description of particle
hoppings, and a new density matrix expansion method where the interacting
lattice slave-particle problem is then turned into a set of overlapping
real-space clusters which are solved self-consistently with appropriate
physical matching constraints at shared lattice sites between clusters.
