Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

Henderson, Thomas M.; Tabrizi, Shadan Ghassemi; Chen, Guo P.; Scuseria, Gustavo E.

doi:10.1063/5.0188155

Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

Journal Article · Thu Feb 08 00:00:00 EST 2024 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0188155· OSTI ID:2349222

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Rice University, Houston, TX (United States); Rice University
Rice University, Houston, TX (United States)

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan–Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree–Fock–Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. Here, we also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.

View Accepted Manuscript (DOE)

Research Organization:: Rice University, Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0001474

OSTI ID:: 2349222

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 160; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Electronic-structure theory
Hartree-Fock-Bogoliubov theory
Heisenberg model
Lie algebras
Mean field theory
Quasiparticle

Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

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