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

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dc.citation.articleNumber231102en_US
dc.citation.issueNumber23en_US
dc.citation.journalTitleThe Journal of Chemical Physicsen_US
dc.citation.volumeNumber158en_US
dc.contributor.authorChen, Guo P.en_US
dc.contributor.authorScuseria, Gustavo E.en_US
dc.contributor.orgChemistryen_US
dc.contributor.orgPhysics and Astronomyen_US
dc.date.accessioned2023-06-23T19:16:01Zen_US
dc.date.available2023-06-23T19:16:01Zen_US
dc.date.issued2023en_US
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.en_US
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.en_US
dc.identifier.doihttps://doi.org/10.1063/5.0156124en_US
dc.identifier.urihttps://hdl.handle.net/1911/114919en_US
dc.language.isoengen_US
dc.publisherAIP Publishingen_US
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.en_US
dc.titleRobust formulation of Wick’s theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctionsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpost-printen_US
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