  The many-body expansion (MBE) is an efficient tool which has a long history
of use for calculating interaction energies, binding energies, lattice
energies, and so on. In the past, applications of MBE to correlation energy
have been unfeasible for large systems, but recent improvements to computing
resources have sparked renewed interest in capturing the correlation energy
using the generalized $n$-th order Bethe-Goldstone equation. In this work, we
extend this approach, originally proposed for a Slater determinant, to a tensor
product state (TPS) based wavefunction. By partitioning the active space into
smaller orbital clusters, our approach starts from a cluster mean field
reference TPS configuration and includes the correlation contribution of the
excited TPSs using the many-body expansion. This method, named cluster
many-body expansion (cMBE), improves the convergence of MBE at lower orders
compared to directly doing a block based MBE from a RHF reference. We present
numerical results for strongly correlated systems such as the one- and
two-dimensional Hubbard models and the chromium dimer. The performance of the
cMBE method is also tested by partitioning the extended $\pi$ space of several
large $\pi$-conjugated systems, including a graphene nano-sheet with a very
large active space of 114 electrons in 114 orbitals, which would require
$10^{66}$ determinants for the exact FCI solution.
