Introduction

The MPSDynamics.jl package provides an easy to use interface for performing tensor network simulations on matrix product states (MPS) and tree tensor network (TTN) states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle (TDVP) method for time evolution. The package also provides strong support for the measurement of observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. The package has been developed with the aim of studying non-Markovian open system dynamics at finite temperature using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm (T-TEDOPA) based on environment chain mapping. However the methods implemented can equally be applied to other areas of physics.

Installation

The package may be installed by typing the following into a Julia REPL

    ] add https://github.com/shareloqs/MPSDynamics.git

Table of Contents

• Introduction
• • Installation
  • Table of Contents
  • Citation
• User Guide
• • Initial State
  • • Matrix Product States
    • Tree Tensor Networks
  • Hamiltonian
  • • Build-in Hamiltonian
    • Convert a MPO from ITensor
    • Tailored MPO
    • Finite Temperature and Custom SD
  • Observables
  • Time-Evolution
  • • One-site TDVP
    • Two-Site TDVP
    • Adaptive One-Site TDVP
  • Data Storage
• The Spin-Boson Model
• • Context
  • The code
• Pure-Dephasing
• • Context
  • The code
  • Bibliography
• Time-dependent Hamiltonian
• • Context
  • The code
• The Anderson Impurity Model
• • Basics of the fermionic chain mapping
  • • Double chain MPO
    • Interleaved chain MPO
  • Code implementation
  • Bibliography
• Inspecting the bath by undoing the chain mapping
• • The code
  • Bibliography
• Proton Transfer Model
• • Context
  • The code
  • Bibliography
• Convergence checks
• • Approximations
  • • Chain length $N$
    • Local dimension $d$
    • Bond dimensions and time evolution
    • Time-step
  • Common pitfalls
  • • Hard cut-off in the spectral density function
  • References
• Theoretical Background
• • Chain-Mapping of bosonic environments
  • • Zero Temperature
    • Finite Temperature with T-TEDOPA
    • Finite temperature with the thermofield transformation
  • Computation of the chain coefficients
  • Tensor Networks
  • • MPS
    • MPO
    • TTN
  • Time-Dependent Variational Principle
  • Bibliography
• List of all methods
• • Matrix Product State (MPS)
  • Tree Tensor Network (TTN)
  • Measure and Obervables
  • Models and Hamiltonians (MPO)
  • Chain-Mapping
  • Dynamics propagation function
  • Advanced
• Developers
• • Simulation Workflow
  • How to Contribute

Citation

If you use the package in your research, please consider citing it. You can add the Zenodo record and the software paper to your BibTex file:

@misc{mpsdynamics_zenodo2021,
	title = {shareloqs/{MPSDynamics}},
	shorttitle = {{MPSDynamics.jl}},
	url = {https://zenodo.org/record/5106435},
	abstract = {Tensor network simulations for finite temperature, open quantum system dynamics},
	publisher = {Zenodo},
	author = {Dunnett, Angus and Lacroix, Thibaut and Le Dé, Brieuc and Riva, Angela},
	year = {2021},
	doi = {10.5281/zenodo.5106435},
}

@article{mpsdynamicsjl_2024,
	title = {{MPSDynamics}.jl: {Tensor} network simulations for finite-temperature (non-{Markovian}) open quantum system dynamics},
	volume = {161},
	issn = {0021-9606},
	shorttitle = {{MPSDynamics}.jl},
	url = {https://doi.org/10.1063/5.0223107},
	doi = {10.1063/5.0223107},
	number = {8},
	journal = {The Journal of Chemical Physics},
	author = {Lacroix, Thibaut and Le Dé, Brieuc and Riva, Angela and Dunnett, Angus J. and Chin, Alex W.},
	month = aug,
	year = {2024},
	pages = {084116},
}