  We derive and implement a new way of solving coupled cluster equations with
lower computational scaling. Our method is based on decomposition of both
amplitudes and two electron integrals, using a combination of tensor
hypercontraction and canonical polyadic decomposition. While the original
theory scales as $O(N^6)$ with respect to the number of basis functions, we
demonstrate numerically that we achieve sub-millihartree difference from the
original theory with $O(N^4)$ scaling. This is accomplished by solving directly
for the factors that decompose the cluster operator. The proposed scheme is
quite general and can be easily extended to other many-body methods.

Chemical Physics;Strongly Correlated Electrons