Geminal replacement models based on AGP

Abstract

The antisymmetrized geminal power (AGP) wavefunction 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.

Correlating AGP on a quantum computer

“…Meanwhile, the AGP wavefunction has emerged as an excellent starting point for this problem [43][44][45]. AGP, which is equivalent to the number-projected BCS wavefunction, [46][47][48] is well known for its ability to describe off-diagonal long-range order without breaking number symmetry [49].…”

Correlating AGP on a quantum computer

“…[42] Meanwhile, the AGP wavefunction has emerged as an excellent starting point for this problem. [42][43][44] AGP, which is equivalent to the number-projected BCS wavefunction, [45][46][47] is well known for its ability to describe off-diagonal long-range order without breaking number symmetry. [48] While AGP is not necessarily a good wavefunction per se, since geminals are not all the same in most physical problems, it has been shown recently that correlated wavefunctions built from AGP are good at describing both the weak and strong pairing correlationsat least in the reduced BCS Hamiltonian.…”

“…[48] While AGP is not necessarily a good wavefunction per se, since geminals are not all the same in most physical problems, it has been shown recently that correlated wavefunctions built from AGP are good at describing both the weak and strong pairing correlationsat least in the reduced BCS Hamiltonian. [42][43][44] There are many qualities that could make AGP an attractive starting point for a more generic Hamiltonian wherein pairing correlations play a role. First, it inherently contains the same number of Slater determinants as doubly occupied configuration interaction (DOCI), [36,[49][50][51] yet it can be optimized with mean-field cost, i.e.…”

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis

“…[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Henderson, Scuseria, and their co-authors are developing a mean-field theory built upon the antisymmetrized geminal power (AGP). 20 In particular, they have found an effective algorithm for evaluating the necessary reduced density matrix (RDM) elements, 21 strategies to include linearly-independent excitations along with their AGP mean-field, 22 methods to add dynamic correlation, 23 , computed properties at finite temperature 24 and have employed it on a quantum computer. 25 They have applied their model to the reduced Bardeen-Cooper-Schrieffer 26,27 (BCS) pairing model.…”