2019/03/31 by Hugh G. A. Burton, Alex J. W. Thom, Pierre-François Loos +1
Mathematics · Physics and Astronomy · #Eigenfunction #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hartree–Fock method #Hermitian matrix #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Wave function #cond-mat.str-el #math-ph #math.MP #physics.atom-ph #physics.chem-ph #quant-ph
paper · pdf · doi:10.1021/acs.jctc.9b00289
published as J. Chem. Theory Comput. 15, 4374 (2019) · 12 pages, 5 figures
arxiv created 2019/05/21 · openalex publication_date 2019/06/05 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
PT-symmetry—invariance with respect to combined space reflection P and time reversal T—provides a weaker condition than (Dirac) Hermiticity for ensuring a real energy spectrum of a general non-Hermitian Hamiltonian. PT-symmetric Hamiltonians therefore form an intermediate class between Hermitian and non-Hermitian Hamiltonians. In this work, we derive the conditions for PT-symmetry in the context of electronic structure theory and, specifically, within the Hartree–Fock (HF) approximation. We show that the HF orbitals are symmetric with respect to the PT operator if and only if the effective Fock Hamiltonian is PT-symmetric, and vice versa. By extension, if an optimal self-consistent solution is invariant under PT, then its eigenvalues and corresponding HF energy must be real. Moreover, we demonstrate how one can construct explicitly PT-symmetric Slater determinants by forming PT-doublets (i.e., pairing each occupied orbital with its PT-transformed analogue), allowing PT-symmetry to be conserved throughout the self-consistent process. Finally, considering the H 2 molecule as an illustrative example, we observe PT-symmetry in the HF energy landscape and find that the spatially symmetry-broken unrestricted HF wave functions (i.e., diradical configurations) are PT-symmetric, while the spatially symmetry-broken restricted HF wave functions (i.e., ionic configurations) break PT-symmetry.