Fundamental limitations of the eigenvalue continuation approach

In this work, we show that the eigenvalue continuation approach introduced recently by Frame et al. [Phys. Rev. Lett. 121, 032501 (2018), 10.1103/PhysRevLett.121.032501], 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.