Computing vibrational eigenstates with tree tensor network states (TTNS)

Area of Science:

• Quantum chemistry
• Computational physics
• Spectroscopy

Background:

• Vibrational spectra are crucial for understanding molecular properties.
• Tree tensor network states (TTNSs) offer a powerful ansatz for quantum many-body problems.
• Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) is a common method for such calculations.

Purpose of the Study:

• To present a novel algorithm for computing vibrational eigenstates using TTNSs.
• To apply and validate this method for the vibrational spectrum of acetonitrile (CH3CN).
• To compare the performance of TTNSs with matrix product states (MPSs).

Main Methods:

• Utilizing a density matrix renormalization group (DMRG)-based algorithm for eigenstate computation.
• Implementing TTNSs as the underlying ansatz, related to ML-MCTDH.
• Comparing TTNSs against MPSs, the ansatz used in DMRG.

Main Results:

• The TTNS-based algorithm achieves high accuracy for the vibrational spectrum of acetonitrile.
• The presented optimization scheme demonstrates significantly faster convergence compared to ML-MCTDH.
• No substantial advantage of TTNS over MPS was observed for this specific system.
• Adaptive bond dimension significantly reduces parameter count for both TTNS and MPS.

Conclusions:

• TTNSs provide an effective approach for calculating vibrational spectra.
• The DMRG-based optimization scheme offers improved convergence rates.
• Further procedures are proposed for optimizing tree structures in TTNS calculations.