Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.06250 · Physical Review A

Configuration interaction with antisymmetrized geminal powers

Wataru Uemura, Shusuke Kasamatsu, Osamu Sugino

Published Jun 16, 2015• 13 citations
arXivHTMLPDF

Abstract

To avoid the combinatorial computational cost of configuration interaction (CI), we previously introduced the symmetric tensor decomposition CI (STD-CI) method, which takes advantage of the antisymmetric nature of the electronic wave function and expresses the CI coefficients compactly as a series of Kronecker product states (STD series) [W. Uemura and O. Sugino, Phys. Rev. Lett. 109, 253001 (2012)]. Here we extend the variational degrees of freedom by using different molecular orbitals for different terms in the STD series. This scheme is equivalent to the linear combination of the Hartree-Fock-Bogoliubov state or the antisymmetrized geminal powers (AGPs). The total energy converges very rapidly within 0.72 $\ensuremath{\mu}\mathrm{hartree}$ taking only 10 terms for the water molecule, and the convergence is likewise fast for Hubbard tetramers. The computational cost scales as the fifth power of the number of electrons and the square of the number of terms in the STD series, indicating the promise of this AGP-based scheme for highly accurate and efficient computation of quantum systems.

DOI
10.1103/physreva.91.062504

Related papers

Description of fermionic wavefunctions by symmetric tensor decomposition

渉 植村

There are a number of evidences and findings in quantum electronic systems in the last a few decades, such as the high Tc superconductivity in cuprates and the colossal magnetoresistance in perovskite oxides, etc.Much effort has been paid to understand the variety of challenging phenomena in condensed matter physics, but we still lack a unified and indisputable theoretical framework that can explain and predict most of these experimental facts.The situation of the theoretical understanding for quantum many body systems has been much refreshed after the discovery of Density Matrix Renormalization Group (DMRG) method in 1992.Since then, numerical and mathematical researches in the so called tensor network frameworks have attracted considerable attention.We focus on theoretical and numerical approaches toward the tensor network framework that make use of quantum information theory and are applicable to quantum chemistry.The purpose of this thesis is to give a tensor network framework that explicitly considers the antisymmetry of the electronic wavefunction contrary to most of the previous works.With a proper consideration of the antisymmetry of the wavefunction, we can dramatically reduce the number of states constituting the total wavefunction and improve the speed of numerical calculation and enhance the convergence of the resulting energy.In chapter 3, we introduce our recently published wavefunction theory where tensor network of the wavefunction is treated using the symmetric tensor decomposition framework with the antisymmetry of the wavefunction explicitly taken into account.This scheme is based on the configuration interaction (CI) which is a versatile wavefunction theory for interacting fermions but involving an extremely long CI series.Using a symmetric tensor decomposition (STD) method, we convert the CI series into a compact and numerically tractable form.The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested using small molecules.Provided that the length of the STD-CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full-CI with enhanced practicability.In Chapter 4, we introduce an improvement of STD-CI.In the Extended STD (ESTD) scheme, the variational degree of freedom in the wavefunction is dramatically extended.Therefore we can expect a considerable improvement in the convergence of the energy in ESTD.And also, in ESTD we can calculate the expectation value of the energy and the first derivatives with a calculation cost proportional to N 5 , while the original scaling in STD-CI is N 6 , where N is the number of electrons.This immediately means that we can dramatically extend the size of the systems that we can treat with ESTD, compared with STD-CI.In ESTD, the wavefunction is given as a linear combination of the Antisymmetrized Geminal Powers (AGP), and the norm and energy are given through a simple formalism based on Pfaffian.We provide a comparison of numerical results of the water molecule and the Hubbard model that indicates the numerical superiority of ESTD with respect to STD-CI.In future we expect to treat larger systems with ESTD, including three dimensional periodic systems.Such calculations will be propelled by the fact that in ESTD we can treat non orthogonal basis sets without taking orthonormalization, which is a procedure that significantly complicates large-scale calculations.

•Mar 24, 2014•0 citations

Configuration interaction extension of AGP for incorporating inter-geminal correlations

Airi Kawasaki, Fei Gao, Gustavo E. Scuseria

In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter $τ$, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H$_2$O and N$_2$ demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.

arXiv:2604.14115•Apr 15, 2026•0 citations

Configuration interaction extension of AGP for incorporating inter-geminal correlations

Airi Kawasaki, Fei Gao, Gustavo E. Scuseria

In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter τ, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H2O and N2 demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.

The Journal of Chemical Physics•Jun 17, 2026•0 citations

Symmetric Tensor Decomposition Description of Fermionic Many-Body Wave Functions

Wataru Uemura, Osamu Sugino

The configuration interaction (CI) is a versatile wave function theory for interacting fermions, but it involves an extremely long CI series. Using a symmetric tensor decomposition method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested by using small molecules. Provided that the length of the symmetric tensor decomposition CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full CI with enhanced practicability.

arXiv:1208.1082•Physical Review Letters•Dec 21, 2012•9 citations

Antisymmetrized geminal powers with larger chemical basis sets

Wataru Uemura, Takahito Nakajima

In previous research, we tested the wave-function format of a linear combination of several antisymmetrized geminal power states. A numerical problem in the geminal matrices was noted, which made the total energies of electronic systems with large numbers of electrons unstable. The underlying cause was found to be the large cancellation term in the geminal power series. We have obtained a format to resolve this problem for the case of total energies and partly for the first-order derivatives within the antisymmetrized geminal power states. By using this formalism, we have calculated the ground-state energies for several electronic systems, including the usage of a larger chemical basis set. The results are, in some cases, very close to the exact result, especially for one-dimensional Hubbard systems. Our result for a water molecule with the Dunning double zeta basis set is better than the configuration-interaction singles and doubles energy and approaches the coupled cluster singles and doubles energy.

arXiv:1810.13143•Physical Review A•Jan 28, 2019•7 citations

Geminal-based configuration interaction

Thomas M. Henderson, Gustavo E. Scuseria

The antisymmetrized geminal power (AGP) wave function has a long history and considerable conceptual appeal, but in many situations its accuracy is wanting. Here, we consider a form of configuration interaction (CI) based upon the AGP wave function and take advantage of its killing operators to construct an excitation manifold. Our geminal CI reduces to standard single-determinant-based CI in the limit in which AGP reduces to a single determinant. It substantially improves upon AGP in the reduced BCS Hamiltonian, which serves as a prototype for the kinds of strong pairing correlations relevant in Bardeen-Cooper-Schrieffer-style superconductivity. Moreover, our geminal CI naturally generalizes to add correlation to more general geminal-based wave functions than AGP.

arXiv:1906.11361•The Journal of Chemical Physics•Aug 2, 2019•47 citations
To avoid the combinatorial computational cost of configuration interaction (CI), we previously introduced the symmetric tensor decomposition CI (STD-CI) method, which takes advantage of the antisymmetric nature of the electronic wave function and expresses the CI coefficients compactly as a series of Kronecker product states (STD series) [W. Uemura and O. Sugino, Phys. Rev. Lett. 109, 253001 (2012)]. Here we extend the variational degrees of freedom by using different molecular orbitals for different terms in the STD series. This scheme is equivalent to the linear combination of the Hartree-Fock-Bogoliubov state or the antisymmetrized geminal powers (AGPs). The total energy converges very rapidly within 0.72 \ensuremathμhartree\ensuremath{\mu}\mathrm{hartree}\ensuremathμhartree taking only 10 terms for the water molecule, and the convergence is likewise fast for Hubbard tetramers. The computational cost scales as the fifth power of the number of electrons and the square of the number of terms in the STD series, indicating the promise of this AGP-based scheme for highly accurate and efficient computation of quantum systems.
There are a number of evidences and findings in quantum electronic systems in the last a few decades, such as the high Tc superconductivity in cuprates and the colossal magnetoresistance in perovskite oxides, etc.Much effort has been paid to understand the variety of challenging phenomena in condensed matter physics, but we still lack a unified and indisputable theoretical framework that can explain and predict most of these experimental facts.The situation of the theoretical understanding for quantum many body systems has been much refreshed after the discovery of Density Matrix Renormalization Group (DMRG) method in 1992.Since then, numerical and mathematical researches in the so called tensor network frameworks have attracted considerable attention.We focus on theoretical and numerical approaches toward the tensor network framework that make use of quantum information theory and are applicable to quantum chemistry.The purpose of this thesis is to give a tensor network framework that explicitly considers the antisymmetry of the electronic wavefunction contrary to most of the previous works.With a proper consideration of the antisymmetry of the wavefunction, we can dramatically reduce the number of states constituting the total wavefunction and improve the speed of numerical calculation and enhance the convergence of the resulting energy.In chapter 3, we introduce our recently published wavefunction theory where tensor network of the wavefunction is treated using the symmetric tensor decomposition framework with the antisymmetry of the wavefunction explicitly taken into account.This scheme is based on the configuration interaction (CI) which is a versatile wavefunction theory for interacting fermions but involving an extremely long CI series.Using a symmetric tensor decomposition (STD) method, we convert the CI series into a compact and numerically tractable form.The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested using small molecules.Provided that the length of the STD-CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full-CI with enhanced practicability.In Chapter 4, we introduce an improvement of STD-CI.In the Extended STD (ESTD) scheme, the variational degree of freedom in the wavefunction is dramatically extended.Therefore we can expect a considerable improvement in the convergence of the energy in ESTD.And also, in ESTD we can calculate the expectation value of the energy and the first derivatives with a calculation cost proportional to N 5 , while the original scaling in STD-CI is N 6 , where N is the number of electrons.This immediately means that we can dramatically extend the size of the systems that we can treat with ESTD, compared with STD-CI.In ESTD, the wavefunction is given as a linear combination of the Antisymmetrized Geminal Powers (AGP), and the norm and energy are given through a simple formalism based on Pfaffian.We provide a comparison of numerical results of the water molecule and the Hubbard model that indicates the numerical superiority of ESTD with respect to STD-CI.In future we expect to treat larger systems with ESTD, including three dimensional periodic systems.Such calculations will be propelled by the fact that in ESTD we can treat non orthogonal basis sets without taking orthonormalization, which is a procedure that significantly complicates large-scale calculations.
In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter τττ, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H2_22​O and N2_22​ demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.
In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter τ, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H2O and N2 demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.
The configuration interaction (CI) is a versatile wave function theory for interacting fermions, but it involves an extremely long CI series. Using a symmetric tensor decomposition method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested by using small molecules. Provided that the length of the symmetric tensor decomposition CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full CI with enhanced practicability.
In previous research, we tested the wave-function format of a linear combination of several antisymmetrized geminal power states. A numerical problem in the geminal matrices was noted, which made the total energies of electronic systems with large numbers of electrons unstable. The underlying cause was found to be the large cancellation term in the geminal power series. We have obtained a format to resolve this problem for the case of total energies and partly for the first-order derivatives within the antisymmetrized geminal power states. By using this formalism, we have calculated the ground-state energies for several electronic systems, including the usage of a larger chemical basis set. The results are, in some cases, very close to the exact result, especially for one-dimensional Hubbard systems. Our result for a water molecule with the Dunning double zeta basis set is better than the configuration-interaction singles and doubles energy and approaches the coupled cluster singles and doubles energy.
The antisymmetrized geminal power (AGP) wave function has a long history and considerable conceptual appeal, but in many situations its accuracy is wanting. Here, we consider a form of configuration interaction (CI) based upon the AGP wave function and take advantage of its killing operators to construct an excitation manifold. Our geminal CI reduces to standard single-determinant-based CI in the limit in which AGP reduces to a single determinant. It substantially improves upon AGP in the reduced BCS Hamiltonian, which serves as a prototype for the kinds of strong pairing correlations relevant in Bardeen-Cooper-Schrieffer-style superconductivity. Moreover, our geminal CI naturally generalizes to add correlation to more general geminal-based wave functions than AGP.