Geminal Replacement Models Based on AGP

Abstract

The antisymmetrized geminal power (AGP) wave function has a long history and is known by different names in various chemical and physical problems. There has been recent interest in using AGP as a starting point for strongly correlated electrons. Here, we show that in a seniority-conserving regime, different AGP-based correlator representations based on generators of the algebra, killing operators, and geminal replacement operators are all equivalent. We implement one representation that uses number operators as correlators and has linearly independent curvilinear metrics to distinguish the regions of Hilbert space. This correlation method called J-CI provides excellent accuracy in energies when applied to the pairing Hamiltonian.

Construction of linearly independent non-orthogonal AGP states

“…In a series of papers, [2][3][4][5][6] our group has explored abandoning Slater determinants as the many-electron basis and proposed instead working with wave functions where the basic building blocks are two-electron functions called geminals, 7 instead of one-electron spin-orbitals. Specifically, the exact wave function can be written in the basis of identical geminal product states known as the antisymmetrized geminal power (AGP), 8 which can be obtained as the number-projected Bardeen-Cooper-Schrieffer (PBCS) wave function.…”

“…9 AGP is variationally more flexible than a Slater determinant and is the simplest wave function supporting off-diagonal long-range order in a number-conserving framework. 10 Correlated methods on an AGP reference accurately describe strong pairing interactions, [2][3][4][5][6] and many correlated AGP models based on different correlators are equivalent since the wave function is essentially expanded in AGP and states replacing one or more geminals. 4 While these constructions work well, they become increasingly challenging as we replace more geminals.…”

“…Rather than writing the wave function in terms of AGP and operators that replace geminals, we write the wave function as a linear combination of AGPs (LC-AGP), 4,11,12 which has the advantage that matrix elements between two different AGP states are simple. LC-AGP is related to the symmetric tensor decomposition of the exact wave function, 4,11 and non-orthogonal construction of AGP bases is natural due to the close connection between AGPs and elementary symmetric polynomials (ESPs). 13 Given a set of AGPs, optimizing the expansion coefficients in LC-AGP is easily done as a non-orthogonal configuration interaction.…”

“…15 Numerical issues with full variational optimization of LC-AGP, which would require optimizing both configuration and geminal coefficients of individual states, have been observed in the literature. 4,11 For this reason, we pursue a different goal in this paper. Rather than optimizing AGP states in an LC-AGP, we wish to construct a linearly independent set of nonorthogonal AGP states such that the LC-AGP identically reproduces the geminal replacement (GR) theories we have considered in previous work.…”

Variational coupled cluster for ground and excited states

“…Note that pCCD is equivalent to the antisymmetric product of 1-reference orbital geminals (AP1roG) [65][66][67][68][69][70][71][72][73][74][75][76] which has been designed as a computationally tractable approximation to the antisymmetric product of geminals (APG), 77,78 a method that has been recently further explored by the group of Scuseria. [79][80][81][82][83][84] Because the seniority-zero subspace is not invariant to orbital rotations, one must energetically optimize the orbitals to obtain the optimal pairing scheme, (i.e., the orbital set that minimizes the energy in the seniority-zero subspace). 57 In Ref.…”