# 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…

## 14 Citations

### Density matrices of seniority-zero geminal wavefunctions.

- PhysicsThe Journal of chemical physics
- 2022

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.

- PhysicsThe Journal of chemical physics
- 2020

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.

- MathematicsJournal of chemical theory and computation
- 2020

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

- Computer Science, Physics
- 2020

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.

- PhysicsThe Journal of chemical physics
- 2020

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.

- ChemistryThe Journal of chemical physics
- 2021

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

- PhysicsMolecular Physics
- 2022

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

- PhysicsJournal of Mathematical Chemistry
- 2020

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.

- PhysicsThe Journal of chemical physics
- 2020

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.

- PhysicsThe Journal of chemical physics
- 2022

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…

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