An efficient Julia framework for hierarchical equations of motion in open quantum systems

The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment interaction with the HEOM method usually results in time-consuming cal...

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Bibliographic Details
Published in:Communications physics 2023-10, Vol.6 (1), p.313-14, Article 313
Main Authors: Huang, Yi-Te, Kuo, Po-Chen, Lambert, Neill, Cirio, Mauro, Cross, Simon, Yang, Shen-Liang, Nori, Franco, Chen, Yueh-Nan
Format: Article
Language:English
Subjects:
639/638/440
639/766/1130
639/766/483/3926
639/766/483/481
Complexity
Equations of motion
Open source software
Physics
Physics and Astronomy
Public domain
Software packages
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Summary:The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment interaction with the HEOM method usually results in time-consuming calculations and a large memory cost. Here, we introduce an open-source software package called HierarchicalEOM.jl: a Julia framework integrating the HEOM approach. HierarchicalEOM.jl features a collection of methods to compute bosonic and fermionic spectra, stationary states, and the full dynamics in the extended space of all auxiliary density operators (ADOs). The required handling of the ADOs multi-indexes is achieved through a user-friendly interface. We exemplify the functionalities of the package by analyzing a single impurity Anderson model, and an ultra-strongly coupled charge-cavity system interacting with bosonic and fermionic reservoirs. HierarchicalEOM.jl achieves a significant speedup with respect to the corresponding method in the Quantum Toolbox in Python (QuTiP), upon which this package is founded. The hierarchical equations of motion approach is useful for the non-perturbative study of complex open quantum systems, which are simultaneously coupled to both bosonic and fermionic environments. To tackle these systems, the authors introduce an open-source software package (HierarchicalEOM.jl), characterized by a notable speed and accessibility to new users.
ISSN:2399-3650
2399-3650
DOI:10.1038/s42005-023-01427-2