Fundamental limitations of the eigenvalue continuation approach

TL;DR

This paper reveals fundamental limitations of the eigenvalue continuation method in strongly correlated many-body systems, demonstrating it cannot surpass the accuracy of sampling states and requires complementary methods for validation.

Contribution

It identifies intrinsic limitations of the eigenvalue continuation approach in strongly correlated systems and illustrates these with a simple model, highlighting the need for supplementary methods.

Findings

Eigenvalue continuation cannot surpass sampling accuracy.

Limitations are demonstrated with a simple fermionic system.

Additional methods are necessary for validation.

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.