WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains

TL;DR

WaveTrain is an open-source Python package that efficiently simulates chain-like quantum systems using tensor train representations, enabling scalable quantum dynamics analysis with visualization features.

Contribution

It introduces a tensor train-based framework for simulating chain-like quantum systems, reducing computational complexity and supporting classical, quantum, and mixed dynamics.

Findings

Tensor train ranks depend weakly on chain length, enabling near-linear scaling.

Efficient solvers for eigenvalue and differential equations are integrated.

Visualization tools support real-time quantum dynamics analysis.

Abstract

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit-tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schroedinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics on the fly, with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions, and with NN interactions only.