Robust formulation of Wick’s theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctions

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dc.citation.articleNumber231102
dc.citation.issueNumber23
dc.citation.journalTitleThe Journal of Chemical Physics
dc.citation.volumeNumber158
dc.contributor.authorChen, Guo P.
dc.contributor.authorScuseria, Gustavo E.
dc.date.accessioned2023-06-23T19:16:01Z
dc.date.available2023-06-23T19:16:01Z
dc.date.issued2023
dc.description.abstractNumerical 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 Communication, 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.
dc.identifier.citationChen, Guo P. and Scuseria, Gustavo E.. "Robust formulation of Wick’s theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctions." <i>The Journal of Chemical Physics,</i> 158, no. 23 (2023) AIP Publishing: https://doi.org/10.1063/5.0156124.
dc.identifier.doihttps://doi.org/10.1063/5.0156124
dc.identifier.urihttps://hdl.handle.net/1911/114919
dc.language.isoeng
dc.publisherAIP Publishing
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by the authors. Published under an exclusive license by AIP Publishing.
dc.titleRobust formulation of Wick’s theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctions
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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