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Computing vibrational eigenstates with tree tensor network states (TTNS).

Henrik R Larsson1

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

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|November 30, 2019
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Summary

We compute vibrational spectra using tree tensor network states (TTNSs) and a density matrix renormalization group (DMRG) algorithm. This method offers faster convergence than ML-MCTDH, with TTNS and matrix product states (MPSs) showing similar performance for acetonitrile.

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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.