A power series approximation in symmetry projected coupled cluster theory

Abstract

Projected Hartree–Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. On the other hand, single-reference methods, such as configuration interaction or coupled cluster theory, can handle weakly correlated problems but cannot properly account for strong correlations. Ideally, we would like to combine these techniques in a symmetry-projected coupled cluster approach, but this is far from straightforward. In this work, we provide an alternative formulation to identify the so-called disentangled cluster operators, which arise when we combine these two methodological strands. Our formulation shows promising results for model systems and small molecules.

Combining Complex Conjugation, Time-Reversal, and Spin-Flip Symmetry Projection of Coupled Cluster Wave Functions

“…On the other hand, as discussed elsewhere, ,,, projected CC has a problem with what we call gauge invariances. These are numerical invariances of the algebraic equations that leave observables unchanged.…”

“…We refer to this approach as the disentangled cluster approximation, although we note that the approximation is not in writing the product of exponentials in terms of a single exponential excitation operator W but in truncating W (which consists of a normalization constant and all possible excitations) to a lower operator rank. We have considered various approaches to extract an approximate W from V and T , , and here we just match the power series expansion of e W |0⟩ in terms of W to that of normale V normale T * | 0 ⟩ in terms of T * . For more details consult ref .…”

“…We have considered various approaches to extract an approximate W from V and T , , and here we just match the power series expansion of e W |0⟩ in terms of W to that of normale V normale T * | 0 ⟩ in terms of T * . For more details consult ref . We note that the effects of single excitations T 1 can be evaluated without approximation.…”

“…Previous work has established many symmetry-projected wave function methods including Hartree–Fock, , configuration interaction, coupled cluster theory, − and perturbation theory . Most of this work has focused on the projection of spin symmetry, although the projection of number symmetry is frequently used in nuclear physics .…”

AGP-based unitary coupled cluster theory for quantum computers

“…A remedy for this problem could be to combine symmetry restoration with CC theory [14,15,[41][42][43][44]. Symmetry breaking and restoration has long been studied in nuclear physics and electronic structure theory [7,11,12,45].…”