Excited states from eigenvector continuation: the anharmonic oscillator

Abstract

Eigenvector continuation (EC) has recently attracted a lot attention in nuclear structure and reactions as a variational resummation tool for many-body expansions. While previous applications focused on ground-state energies, excited states can be accessed on equal footing. This work is dedicated to a detailed understanding of the emergence of excited states from the eigenvector continuation approach. For numerical applications the one-dimensional quartic anharmonic oscillator is investigated, which represents a strongly non-perturbative quantum system where the use of standard perturbation techniques break down. We discuss how different choices for the construction of the EC manifold affect the quality of the EC resummation and investigate in detail the results from EC for excited states compared to results from a full diagonalization as a function of the basis-space size.

7 pages, 6 figures, accepted in Phys. Lett. B

References in corpus (6)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Converged ab initio calculations of heavy nuclei
• Global sensitivity analysis of bulk properties of an atomic nucleus
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• In-medium similarity renormalization group with three-body operators
• Fast & accurate emulation of two-body scattering observables without wave functions

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• Reduced basis emulation of pairing in finite systems
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
• IMSRG-Net: A machine learning-based solver for In-Medium Similarity Renormalization Group
• Hartree-Fock emulators for nuclei: Application to charge radii of ${}^{48,52}$Ca
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation