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We present a similarity transformation theory based on a polynomial form of aparticle-hole pair excitation operator. In the weakly correlated limit, thispolynomial becomes an exponential, leading to coupled cluster doubles. In theopposite strongly correlated limit, the polynomial becomes an extended Besselexpansion and yields the projected BCS wavefunction. In between, we interpolateusing a single parameter. The effective Hamiltonian is non-hermitian and thisPolynomial Similarity Transformation Theory follows the philosophy oftraditional coupled cluster, left projecting the transformed Hamiltonian ontosubspaces of the Hilbert space in which the wave function variance is forced tobe zero. Similarly, the interpolation parameter is obtained through minimizingthe next residual in the projective hierarchy. We rationalize and demonstratehow and why coupled cluster doubles is ill suited to the strongly correlatedlimit whereas the Bessel expansion remains well behaved. The model providesaccurate wave functions with energy errors that in its best variant are smallerthan 1\% across all interaction stengths. The numerical cost is polynomial insystem size and the theory can be straightforwardly applied to any realisticHamiltonian.

physical review. b./physical review. b

Polynomial Similarity Transformation Theory: A smooth interpolation  between coupled cluster doubles and projected BCS applied to the reduced BCS  Hamiltonian