Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)

TL;DR

This paper demonstrates that the Hierarchy of Pure States (HOPS) method provides a numerically exact and versatile approach for simulating the dynamics of open quantum systems, especially with sub-Ohmic environments and at various temperatures.

Contribution

It extends HOPS applicability to sub-Ohmic spectral densities and strong coupling regimes, including non-zero temperature effects using a stochastic approach.

Findings

HOPS achieves perfect agreement with other methods for the spin-boson model.

The non-linear HOPS variant is necessary for importance sampling in strong coupling.

Using zero-temperature BCF with stochastic temperature effects is effective at non-zero temperatures.

Abstract

We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and non-zero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the non-linear variant of HOPS. In order to include non-zero temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.