Construction of linearly independent non-orthogonal AGP states

Abstract

We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement (GR) models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction (SCI) method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

Variational theory combining number-projected BCS and coupled-cluster doubles

“…For the moderate values of the pairing strength G considered here (2 to 3 times the value of G cr ) this still allows for an exact particle-number conservation (within the numerical accuracy). This key computational aspect is ensured by the negligible contributions of the high order terms within the PBCS (6) and vCCD sep (19) expansions, due to the small (subunitary) numerical values of their corresponding collective pair amplitudes. All results presented below for L = 60 and L = 100 were obtained upon projecting the particlenumber only within a C 1 = 15 ph-pair subspace for PBCS in Eq.…”

“…In this section we propose a novel efficient algorithm for the evaluation of expectation values on the combined vCCD (w) sep PBCS wavefunction (17). It is based on a representation of the PBCS (7), vCCD sep (19) and vCCD (w) (16) terms as disentangled particle and hole gauge-angle-rotated BCS states.…”

“…which would act as a more natural choice (albeit more computationally challenging) for a regime lacking a well-defined Fermi sea. As a first step one could envision building a multi-separable beyond-ph CCD excitation operator which could be optimized with the very recently developed methods for constructing linearly-independent PBCS states [19].…”

“…This fact was made evident in ultrasmall superconducting grains, where PBCS predicted an abrupt metal-superconductor transition as a function of the grain size [9] while the exact solution showed a smooth crossover dominated by large fluctuations [10]. It was precisely in the field of ultrasmall superconducting grains that the exact solution of the constant pairing Hamiltonian given by Richardson in the sixties [11] was recovered [12] and intensively used as a natural benchmark model for superconducting theories beyond BCS [13][14][15][16][17][18][19][20][21].…”