Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions

Abstract

Numerical difficulties associated with computing matrix elements of operators between Hartree-Fock-Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by zero in the standard formulation of the nonorthogonal Wick's theorem in the limit of vanishing HFB overlap. In this paper, we present a robust formulation of Wick's theorem that stays well-behaved regardless of whether the HFB states are orthogonal or not. This new formulation ensures cancellation between the zeros of the overlap and the poles of the Pfaffian, which appears naturally in fermionic systems. Our formula explicitly eliminates self-interaction, which otherwise causes additional numerical challenges. A computationally efficient version of our formalism enables robust symmetry-projected HFB calculations with the same computational cost as mean-field theories. Moreover, we avoid potentially diverging normalization factors by introducing a robust normalization procedure. The resulting formalism treats even and odd number of particles on equal footing and reduces to Hartree-Fock as a natural limit. As proof of concept, we present a numerically stable and accurate solution to a Jordan-Wigner-transformed Hamiltonian, whose singularities motivated the present work. Our robust formulation of Wick's theorem is a most promising development for methods using quasiparticle vacuum states.

References in corpus (42)

• Particle number projection with effective forces
• Projected Quasiparticle Theory for Molecular Electronic Structure
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Particle-Number Projection and the Density Functional Theory
• Particle-Number Restoration within the Energy Density Functional Formalism
• Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Symmetry restoration in mean-field approaches
• Symmetry-Projected Hartree-Fock-Bogoliubov Equations
• An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
• Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian
• Correlating AGP on a quantum computer
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• Efficient evaluation of AGP reduced density matrices
• Correlating the Antisymmetrized Geminal Power Wave Function
• Geminal replacement models based on AGP
• Exploring non-linear correlators on AGP
• Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
• Generalised Nonorthogonal Matrix Elements: Unifying Wick's Theorem and the Slater-Condon Rules
• Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space
• A new and practical formulation for overlaps of Bogoliubov vacua
• Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions
• A new formulation to calculate general HFB matrix elements through Pfaffian
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Quadrupole Collective States in a Large Single-J Shell
• Construction of linearly independent non-orthogonal AGP states
• AGP-based unitary coupled cluster theory for quantum computers
• Cooper-Pair Condensates with Non-Classical Long-Range Order on Quantum Devices
• N-electron Slater determinants from non-unitary canonical transformations of fermion operators
• Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems
• Minimal matrix product states and generalizations of mean-field and geminal wavefunctions
• Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules
• Configuration Interaction with Antisymmetrized Geminal Powers
• Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems
• Variational theory combining number-projected BCS and coupled-cluster doubles
• Efficient computation of matrix elements of generic Slater determinants
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Generalization of the Bloch-Messiah-Zumino theorem

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• Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems
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• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Numerically Stable Resonating Hartree-Fock
• Jordan-Wigner Transformation for the Description of Strong Correlation in Fermionic Systems
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