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.

arXiv comment7 pages, 6 figures, accepted in Phys. Lett. B

References in corpus (27)

• Coupled-cluster computations of atomic nuclei
• From low-momentum interactions to nuclear structure
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Structure of the lightest tin isotopes
• Ab initio limits of atomic nuclei
• Ab Initio Path to Heavy Nuclei
• Leading chiral three-nucleon forces along isotope chains in the calcium region
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• Eigenvector continuation with subspace learning
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Converged ab initio calculations of heavy nuclei
• Global sensitivity analysis of bulk properties of an atomic nucleus
• Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification
• Charge radii of exotic neon and magnesium isotopes
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• In-medium similarity renormalization group with three-body operators
• Efficient emulators for scattering using eigenvector continuation
• Ab initio computation of charge densities for Sn and Xe isotopes
• Improved many-body expansions from eigenvector continuation
• Fast & accurate emulation of two-body scattering observables without wave functions
• Convergence of Eigenvector Continuation
• Pade-resummed high-order perturbation theory for nuclear structure calculations
• Bogoliubov many-body perturbation theory under constraint

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• 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