Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

Abstract

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.

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

“…The same is not true for attractive two-body interactions, where DOCI and pCCD can give very different results [39,42]. This is not to say that the higher-order excitations in DOCI cannot be expressed in terms of the double excitations; this can indeed be done, but to do so one must abandon the exponential parameterization of the wave function [42,43].…”

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

“…It is widely accepted that, while coupled-cluster theory [1][2][3] (CC) has been remarkably successful in capturing accurate dynamical correlation, the use of traditional singlereference (SR) methods is an ill-posed route for static correlation. 4,5 This is because a reference wave function, e.g., Hartree-Fock (HF), is inadequate for strongly correlated systems, and the exponential wave operator eT in SR-CC has to be improved by including higher excitation ranks, entailing a rapid increase in computational cost. This difficulty can be ameliorated by adopting some multiconfiguration (MC) ansatz, for which a complete active space self-consistent field 6,7 (CASSCF) is widely employed; however, the formulation of multireference (MR)-CC is far less straightforward.…”

Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

“…In this communication, building on our work on polynomial similarity transformations (PoSTs), 18 we show how one can cast PHF in terms of particle-hole excitations out of a symmetry-adapted determinant and, moreover, we show how one can optimize the PHF wave function in coupled-cluster-like fashion as opposed to the more traditional variational optimization. We will here consider only what we call SUHF, and will further limit ourselves to projection onto singlet states (s = 0) only, but the theory can be extended to a much more general framework including other quantum numbers and symmetries.…”

“…Previous work on polynomial similarity transformations 18 showed how one could interpolate between the number projected Bardeen-Cooper-Schrieffer and coupled cluster forms of wave function by writing them both in the same language. Rather than interpolating, however, we would like to combine coupled cluster theory and symmetryprojected mean-field methods in a more sophisticated and presumably more correct wave function, a task made more difficult by the very different natures of the two theories (but see Ref.…”