  We present a similarity transformation theory based on a polynomial form of a
particle-hole pair excitation operator. In the weakly correlated limit, this
polynomial becomes an exponential, leading to coupled cluster doubles. In the
opposite strongly correlated limit, the polynomial becomes an extended Bessel
expansion and yields the projected BCS wavefunction. In between, we interpolate
using a single parameter. The effective Hamiltonian is non-hermitian and this
Polynomial Similarity Transformation Theory follows the philosophy of
traditional coupled cluster, left projecting the transformed Hamiltonian onto
subspaces of the Hilbert space in which the wave function variance is forced to
be zero. Similarly, the interpolation parameter is obtained through minimizing
the next residual in the projective hierarchy. We rationalize and demonstrate
how and why coupled cluster doubles is ill suited to the strongly correlated
limit whereas the Bessel expansion remains well behaved. The model provides
accurate wave functions with energy errors that in its best variant are smaller
than 1\% across all interaction stengths. The numerical cost is polynomial in
system size and the theory can be straightforwardly applied to any realistic
Hamiltonian.
