Tree Tensor Networks Methods for Efficient Calculation of Molecular Vibrational Spectra

TL;DR

This paper introduces Tree Tensor Networks (TTNs) for efficient vibrational spectra calculations, exploring various architectures and eigensolvers, achieving sub-wavenumber accuracy with different TTN structures.

Contribution

It develops and benchmarks diverse TTN architectures for vibrational spectra, including implementation of eigensolvers, demonstrating their effectiveness and efficiency.

Findings

Sub-wavenumber accuracy achieved with all TTN structures

MPS and T3NS have similar runtimes

Leaf-only trees require more computational time

Abstract

We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We explore various tree architectures, ranging from the simple linear structure of Matrix Product States (MPS), to trees where only the leaf nodes carry a physical leg -- as seen in the underlying ansatz of the Multilayer Multiconfiguration Time-Dependent Hartree (ML-MCTDH) method -- and further to more general trees in which all nodes are allowed to possess a physical leg. In addition, we implement Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) methods and Inverse Iteration methods as eigensolvers. By means of comprehensive benchmarking of runtime and accuracy, we demonstrate that sub-wavenumber accuracy in vibrational spectra is achievable with all TTN structures. MPS and three-legged tree tensor network states (T3NS) have similar runtimes, whereas leaf-only trees require significantly more time. All numerical simulations were performed using PyTreeNet, a Python package designed for flexible tensor network computations.