Excited states from eigenvector continuation: the anharmonic oscillator

TL;DR

This paper explores how eigenvector continuation can be used to accurately compute excited states in a non-perturbative quantum system, specifically the anharmonic oscillator, expanding its application beyond ground states.

Contribution

It provides a detailed analysis of the emergence of excited states from eigenvector continuation and evaluates the method's effectiveness for a strongly non-perturbative system.

Findings

EC can accurately reproduce excited states compared to full diagonalization.

Choice of EC manifold construction significantly impacts resummation quality.

EC remains effective as basis size increases.

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.