Fundamental limitations of the eigenvalue continuation approach

Abstract

In this work, we show that the eigenvalue continuation approach introduced recently in [Phys. Rev. Lett. {\bf 121}, 032501 (2018)], despite its many advantages, has some fundamental limitations which cannot be overcome when strongly correlated many-body systems are considered. Taking as a working example a very simple system of several fermionic particles confined in a harmonic trap we show that the eigenvector continuation is not able to go beyond the accuracy of the sampling states. We support this observation within a very simple three-level model capturing directly this obstacle. Since mentioned inaccuracy cannot be determined self-consistently within the eigenvalue continuation approach, support from other complementary methods is needed.

arXiv commentAuthors' version accepted for publication

References in corpus (19)

• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• Few-body physics with ultracold atomic and molecular systems in traps
• One-dimensional mixtures of several ultracold atoms: a review
• Eigenvector continuation with subspace learning
• Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons
• Improved many-body expansions from eigenvector continuation
• Quenching small quantum gases: Genesis of the orthogonality catastrophe
• Toward emulating nuclear reactions using eigenvector continuation
• Convergence of Eigenvector Continuation
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Efficient construction of many-body Fock states having the lowest energies
• Variational approach for interacting ultra-cold atoms in arbitrary one-dimensional confinement
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

Cited by in corpus (2)

• Eigenvector Continuation and Projection-Based Emulators
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model