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Numerical quantum mechanics of chain-like systems based on tensor trains

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by Jerome Riedel, Patrick Gelß, and Burkhard Schmidt

Freie Universität Berlin, Germany

Short description

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only (with or without periodic boundary conditions). This Python package is centered around tensor train (TT, or matrix product) representations of quantum-mechanical Hamiltonian operators and (stationary or time-evolving) state vectors. WaveTrain builds on the Python tensor train toolbox scikit_tt, which provides efficient construction methods, storage schemes, as well as solvers for eigenvalue problems and linear differential equations in the TT format.

WaveTrain comprises solvers for time-independent and time-dependent Schrödinger equations employing TT decompositions to construct low-rank representations. Often, the TT ranks of state vectors are found to depend only marginally on the chain length N, which results in the computational effort growing only slightly more than linearly in N, thus mitigating the curse of dimensionality. Thus, WaveTrain complements the existing WavePacket project at SourceForge which does not offer these advantages but which can be used for general Hamiltonians, i.e., without restriction to chain-like systems.

As a complement to the Python classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite ("slow-fast" and/or "heavy-light") systems. Moreover, the graphical capabilities allow visualization of quantum dynamics ‘on the fly’, with a choice of several different graphical representations based on reduced density matrices.


After downloading and installing the Python tensor train toolbox scikit_tt, you can download the latest version of WaveTrain to your local computer by using the 'git clone' command.
Note that a file and a setup.cfg file are included in the package. To install the package simply enter:

git clone 
cd wave_train
python install --user

which subsequently allows to download or upload recent changes later by 'git pull' or 'git push', respectively.

Alternatively, you may install the latest version directly from GitHub:

pip install git+

in which case there is no direct git access. Later changes can be downloaded by the command

pip install --upgrade git+


see our work on coupled excitons and phonons [^1]

[^1]: P. Gelß, R. Klein, S. Matera, B. Schmidt, "Solving the Time-Independent Schrödinger Equation for Chains of Coupled Excitons and Phonons using Tensor Trains", J. Chem. Phys. 156 (2), 024109 (2022)

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