Complex Adiabatic Connection: a Hidden Non-Hermitian Path from Ground to Excited States

Abstract

Processes related to electronically excited states are central in many areas of science, however accurately determining excited-state energies remains a major challenge in theoretical chemistry. Recently, higher energy stationary states of non-linear methods have themselves been proposed as approximations to excited states, although the general understanding of the nature of these solutions remains surprisingly limited. In this Letter, we present an entirely novel approach for exploring and obtaining excited stationary states by exploiting the properties of non-Hermitian Hamiltonians. Our key idea centres on performing analytic continuations of conventional quantum chemistry methods. Considering Hartree--Fock theory as an example, we analytically continue the electron-electron interaction to expose a hidden connectivity of multiple solutions across the complex plane, revealing a close resemblance between Coulson--Fischer points and non-Hermitian degeneracies. Finally, we demonstrate how a ground-state wave function can be morphed naturally into an excited-state wave function by constructing a well-defined complex adiabatic connection.

5 pages, 3 figures

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Cited by in corpus (9)

• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
• Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach
• Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms
• Variations of the Hartree-Fock fractional-spin error for one electron
• Holomorphic Density Functional Theory
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Transient Uniform Electron Gases
• Complex analysis of divergent perturbation theory at finite temperature