Comment on "Numerical Evidence Falsifying Finite-Temperature Many-Body Perturbation Theory"

In this comment we address the preprint of Jha and Hirata (arXiv:1809.10316 [physics.chem-ph]) which claims "Numerical Evidence Falsifying Finite-Temperature Many-Body Perturbation Theory." We agree that finite difference differentiation of the exact grand potential is the correct way to verify the terms in the perturbation expansion. However, it is our suspicion that theoretical errors, uncontrolled numerical errors, and/or errors in their implementation have led Jha and Hirata to incorrectly conclude that finite temperature perturbation theory is incorrect. We show numerical evidence from finite difference differentiation of the grand potential that supports the correctness of finite-temperature perturbation theory.