Flexible scheme to truncate the hierarchy of pure states

TL;DR

This paper introduces new truncation schemes for the hierarchy of pure states (HOPS) in open quantum system modeling, demonstrating improved convergence checks and applicability to molecular aggregate problems.

Contribution

The paper proposes the $n$-mode approximation ($n$MA) for HOPS and explores its convergence properties, enhancing the numerical feasibility of hierarchy truncation methods.

Findings

$n$MA improves convergence checks in HOPS.

Combination of $n$PA and $n$MA achieves convergence in molecular problems.

Truncation schemes enable practical modeling of open quantum systems.

Abstract

The hierarchy of pure states (HOPS) is a wavefunction-based method which can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a 'good' truncation method, where by 'good' we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work we demonstrate the application of the '$n$-particle approximation' ($n$PA) to HOPS. We also introduce a new approximation, which we call the '$n$-mode approximation' ($n$MA). We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy. We show that truncation approximations can be used in combination to achieve convergence in two exemplary problems: absorption and energy transfer of molecular aggregates.