Exploring non-linear correlators on AGP

Abstract

Single-reference methods such as Hartree-Fock-based coupled cluster theory are well known for their accuracy and efficiency for weakly correlated systems. For strongly correlated systems, more sophisticated methods are needed. Recent studies have revealed the potential of the antisymmetrized geminal power (AGP) as an excellent initial reference for the strong correlation problem. While these studies improved on AGP by linear correlators, we explore some non-linear exponential ansätze in this paper. We investigate two approaches in particular. Similar to Phys. Rev. B 91, 041114(R) (2015), we show that the similarity transformed Hamiltonian with a Hilbert-space Jastrow operator is summable to all orders and can be solved over AGP by projecting Schrödinger's equation. The second approach is based on approximating the unitary pair-hopper ansatz recently proposed for application on a quantum computer. We report benchmark numerical calculations against the ground state of the pairing Hamiltonian for both of these approaches.

Construction of linearly independent non-orthogonal AGP states

“…[28][29][30] In contrast, AGP and AGP-based methods are able to capture most of the correlation energies systematically. [2][3][4][5][6] We need to compute overlaps between AGPs to build the LC-AGP metric and need the following transition reduced density matrix (RDM) elements…”

“…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.…”

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

“…There were attempts to interpolate between pCCD and PBCS [8,16] or to diagonalize the pairing Hamiltonian in a subspace defined by the reference PBCS state and different two and four number projected quasiparticle states [24]. Other possible ways to add correlations to the PBCS state were explored in [25,26].…”

Transition density matrices of Richardson-Gaudin states

“…[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] The group of Scuseria are developing a many-body theory for pairs based on the antisymmetrized geminal power (AGP) as a mean-field. [24][25][26][27][28][29][30] Their approach has the advantage that the wavefunction is simple and represents a clear physical picture: condensation of pairs. Their principal application thus far has been the reduced Bardeen-Cooper-Schrieffer (BCS) 31,32 pairing model.…”