Improved many-body expansions from eigenvector continuation

Abstract

Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment of microscopic fermionic systems, it is desirable to obtain accurate results through low-order perturbation theory. In atomic nuclei however, effects such as strong short-range repulsion between nucleons can spoil the convergence of the expansion and make the reliability of perturbation theory unclear. Mathematicians have devised an extensive machinery to overcome the problem of divergent expansions by making use of so-called resummation methods. In large-scale many-body applications such schemes are often of limited use since no a priori analytical knowledge of the expansion is available. We present here eigenvector continuation as an alternative resummation tool that is both efficient and reliable because it is based on robust and simple mathematical principles.

6 pages, 2 figures

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• Fast & accurate emulation of two-body scattering observables without wave functions
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Eigenvector Continuation and Projection-Based Emulators
• Convergence of Eigenvector Continuation
• Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
• Bogoliubov many-body perturbation theory under constraint
• Self-learning Emulators and Eigenvector Continuation
• Thermal behavior as indicator for hyperons in binary neutron star merger remnants
• Eigenvector continuation for emulating and extrapolating two-body resonances
• Excited states from eigenvector continuation: the anharmonic oscillator
• Nuclear Structure at the Crossroads
• Volume extrapolation via eigenvector continuation
• Nuclear-matter saturation and symmetry energy within $\Delta$--full chiral effective field theory
• Reduced basis emulation of pairing in finite systems
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Floating block method for quantum Monte Carlo simulations
• Impact of correlations on nuclear binding energies
• Interpolating many-body wave functions for accelerated molecular dynamics on the near-exact electronic surface
• Trimmed Sampling Algorithm for the Noisy Generalized Eigenvalue Problem
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
• Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description
• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
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• Fundamental limitations of the eigenvalue continuation approach
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• Complex-energy eigenvector continuation for nuclear many-body broad resonances
• Active learning emulators for nuclear two-body scattering in momentum space
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• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations