Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

TL;DR

This paper compares explicit wave function and implicit density matrix methods for simulating dissipative quantum systems, finding the implicit HEOM approach more efficient for baths with exponential decay correlations.

Contribution

It demonstrates the superior efficiency of the TTN-HEOM method over explicit ML-MCTDH in modeling dissipative environments, supported by implementation in the TENSO package.

Findings

TTN-HEOM outperforms ML-MCTDH in efficiency for dissipative baths.

Explicit methods require extensive mode discretization, leading to computational bottlenecks.

TTN-HEOM accurately captures dynamics with fewer auxiliary modes.

Abstract

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM -- rooted in bath correlation function decompositions -- proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna--Matthews--Olson complex model highlight TTN-HEOM's superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.