Comment on "Unified framework for open quantum dynamics with memory"

TL;DR

This comment critiques a recent article claiming a new relationship between GQME and path integral, showing it repeats prior work, misapplies discretization, and overlaps with existing methods like TTM and diagrammatic analysis.

Contribution

The paper clarifies that the recent article's claims are not novel and points out overlaps with established methods and prior research.

Findings

The claimed relationship was previously established in 2020.

The discretization approach used is inconsistent with established decompositions.

The article's analysis overlaps with existing methods like TTM and prior diagrammatic work.

Abstract

A recent article by Ivander, Lindoy and Lee [Nature Communications 15, 8087 (2024)] claims to discover the relationship between the generalized quantum master equation (GQME) and the path integral for a system coupled to a harmonic bath. However, this relationship was already established in 2020 by Makri in the context of the small matrix decomposition of the path integral (SMatPI) [J. Chem. Theory and Comput. 16, 4038 (2020)]. The procedure that this article uses in its Supplementary Information (SI) to obtain the various matrices follows the SMatPI decomposition steps for the alternative Trotter ordering. The absence of endpoint effects in the kernel matrices of the discretized GQME expression for the reduced density matrix (RDM) is the consequence of a crude GQME discretization and is not consistent with the SMatPI decomposition of an auxiliary matrix presented in the SI. This form is identical to the transfer tensor method (TTM) of Cerrillo and Cao [Phys. Rev. Lett. 112, 110401 (2014)]. Further, the Dyck path section of this article follows precisely the diagrammatic analysis developed by Wang and Cai in a recent paper [Communications in Computational Physics 36, 389 (2024)]. We elaborate on these three critiques in this Comment.