Computing vibrational eigenstates with tree tensor network states (TTNS)

TL;DR

This paper introduces a method using tree tensor network states (TTNS) to compute vibrational eigenstates, demonstrating faster convergence than traditional ML-MCTDH and comparing TTNS with matrix product states (MPS) for high-accuracy vibrational spectra.

Contribution

It presents a DMRG-based algorithm for vibrational eigenstates using TTNS, compares TTNS and MPS, and proposes a procedure to optimize tree structures.

Findings

Faster convergence of the optimization scheme compared to ML-MCTDH.

No major advantage of TTNS over MPS for the studied system.

Adaptive bond dimension reduces the number of parameters needed.

Abstract

We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG). We apply this to compute the vibrational spectrum of acetonitrile (CH$_3$CN) to high accuracy and compare TTNSs with matrix product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme converges much faster than ML-MCTDH-based optimization. For this particular system, we found no major advantage of the more general TTNS over MPS. We highlight that for both TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of required parameters. We furthermore propose a procedure to find good trees.