2020/12/31 by Antoine Marie, Hugh G. A. Burton, Pierre-François Loos +1
Mathematics · Physics and Astronomy · #Complex plane #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #Theoretical physics #cond-mat.str-el #physics.chem-ph #physics.comp-ph #quant-ph
paper · pdf · doi:10.1088/1361-648x/abe795
published as J. Phys.: Condens. Matter 33, 283001 (2021) · 22 page, 14 figures, 4 tables
arxiv created 2021/02/02 · openalex publication_date 2021/02/18 · arxiv updated 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree-Fock approximation and Rayleigh-Schrödinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within Møller-Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Padé and quadratic approximants) that can improve the overall accuracy of the Møller-Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.