Matrix product state formulation of the multiconfiguration time-dependent Hartree theory

TL;DR

This paper introduces a matrix product state (MPS) approach to the multiconfiguration time-dependent Hartree (MCTDH) theory, enabling efficient quantum dynamics simulations of complex molecular systems by reducing computational costs.

Contribution

The authors develop an MPS-based formulation of MCTDH, deriving equations of motion and an efficient evaluation method, advancing the computational capabilities of quantum dynamics simulations.

Findings

Demonstrated improved efficiency in quantum dynamics simulations

Achieved convergence with reduced computational resources

Validated approach on extended excitonic molecular systems

Abstract

A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized in the MCTDH ansatz and thus results in an exponential increase of the computational cost, is parametrized by the MPS form. Equations of motion based on the Dirac-Frenkel time-dependent variational principle is derived by using the tangent space projection and the projector-splitting technique for the MPS, which have been recently developed. The mean-field operators, which appears in the equation of motion of the MCTDH single particle functions, are written in terms of the MPS form and efficiently evaluated by a sweep algorithm that is similar to the DMRG sweep. The efficiency and convergence of the MPS formulation to the MCTDH are demonstrated by quantum dynamics simulations of extended excitonic molecular systems.