WaveTrain: A Python package for numerical quantum mechanics of chain-like systems based on tensor trains.

Area of Science:

• Computational Physics
• Quantum Mechanics
• Software Development

Background:

• Numerical simulations of quantum systems are computationally intensive, especially for long chains.
• Existing methods often struggle with scalability due to the curse of dimensionality.
• Efficient algorithms are needed for simulating complex quantum dynamics.

Purpose of the Study:

• Introduce WaveTrain, an open-source software package for numerical simulations of chain-like quantum systems.
• Demonstrate how tensor train format representations mitigate the curse of dimensionality.
• Provide tools for classical and quantum-classical dynamics, alongside visualization capabilities.

Main Methods:

• Utilizes the tensor train (matrix product) format for Hamiltonian operators and state vectors.
• Builds upon the Scikit_tt Python toolbox for efficient TT format operations.
• Employs solvers for eigenvalue problems and linear differential equations for Schrödinger equations.

Main Results:

• Tensor-train ranks of state vectors show marginal dependence on chain length (N).
• Computational effort scales slightly more than linearly with N, effectively mitigating the curse of dimensionality.
• WaveTrain supports full quantum mechanics, classical, and mixed quantum-classical dynamics.

Conclusions:

• WaveTrain offers an efficient and scalable solution for simulating chain-like quantum systems.
• The software facilitates the study of phenomena like excitonic energy transport.
• Version 1.0 is freely available, with ongoing development and demonstration examples provided.