Efficient evaluation of AGP reduced density matrices.

@article{Khamoshi2019EfficientEO,
  title={Efficient evaluation of AGP reduced density matrices.},
  author={Armin Khamoshi and Thomas M. Henderson and Gustavo E. Scuseria},
  journal={The Journal of chemical physics},
  year={2019},
  volume={151 18},
  pages={
          184103
        }
}
We propose and implement an algorithm to calculate the norm and reduced density matrices (RDMs) of the antisymmetrized geminal power of any rank with polynomial cost. Our method scales quadratically per element of the RDMs. Numerical tests indicate that our method is very fast and capable of treating systems with a few thousand orbitals and hundreds of electrons reliably in double-precision. In addition, we present reconstruction formulas that allow one to decompose higher order RDMs in terms… 

Figures from this paper

Density matrices of seniority-zero geminal wavefunctions.

Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick's theorem for fermions or

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

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a variational wavefunction ansatz in quantum chemistry and optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs are reported.

Geminal replacement models based on AGP.

It is shown 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.

Correlating AGP on a quantum computer

This work proposes and implements a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian, showing highly accurate ground state energies in all correlation regimes of this model Hamiltonian.

Correlating the antisymmetrized geminal power wave function.

This work discusses how the antisymmetrized geminal power wave function might be used as a reference state for a more sophisticated correlation technique such as configuration interaction, coupled cluster theory, or the random phase approximation.

Variational coupled cluster for ground and excited states.

The structure of the energy landscape of variational CC is explored and it is compared with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD).

On the size consistency problem for anti-symmetrised geminal power wave function ansatz

It is shown that the accepted proof of the anti-symmetrised geminal power (AGP) wave functions lack of size consistency is not general enough to constitute a proof for the size consistency of the AGP

Richardson-Gaudin geminal wavefunctions in a Slater determinant basis

Geminal wavefunctions have been employed to model strongly-correlated electrons. These wavefunctions represent products of weakly-correlated pairs of electrons and reasonable approximations are

Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems.

A wave function representation for the canonical ensemble thermal density matrix is presented by projecting the thermofield double state against the desired number of particles by number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model.

Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These

References

SHOWING 1-10 OF 32 REFERENCES

Optimization of density matrix functionals by the Hartree–Fock–Bogoliubov method

It is demonstrated that the “corrected Hartree–Fock” (CHF) density matrix functional proposed by Csanyi and Arias is identical with the Hartree–Fock–Bogoliubov (HFB) functional of the generalized

Calculation of optimal generalized antisymmetrized geminal-power (projected—Bardeen-Cooper-Schrieffer) functions and their associated excitation spectrum

The generalized antisymmetrized geminal-power (GAGP) function, shown to be the ground state for the oneparticle-hole propagator, can be computed using the rather simple properties of its reduced

Geminal-based configuration interaction

This work considers a form of configuration interaction based upon the AGP wave function and taking advantage of its killing operators to construct an excitation manifold, reducing to standard single-determinant--based CI in the limit in which AGP reduces to a single determinant.

A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals.

This work focuses on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied, and gives good results for atoms and small molecules.

Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers

Functions which can be expressed as an antisymmetrized power of a single two‐particle function (a geminal) occur in the BCS ansatz. They constitute a comparatively tractable generalization of a

Projected quasiparticle theory for molecular electronic structure.

This work derives and implements symmetry-projected Hartree-Fock-Bogoliubov equations and applies them to the molecular electronic structure problem, showing that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost.

Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy.

It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion, and the energy relevance of the seniority zero sector increases dramatically if orbitals of broken spatial symmetry are allowed in the wave function construction.

A new approach to density matrix functional theory

Starting from a pair-excitation multiconfiguration self-consistent field approach considering pairwise excitations of two electrons of opposite spin from a single occupied molecular orbital to a