Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto 606-8502, Japan.
J Chem Phys. 2018 Nov 21;149(19):194114. doi: 10.1063/1.5051498.
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 in 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 appear 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 density-matrix renormalized group sweep. The efficiency and convergence of the MPS approximation to the MCTDH are demonstrated by quantum dynamics simulations of extended excitonic molecular systems.
提出了多组态含时哈特里（MCTDH）理论的矩阵乘积态表述。声子自由度的直积张成的 Hilbert 空间在 MCTDH 假设中线性参数化，从而导致计算成本呈指数增长，通过矩阵乘积态（MPS）进行参数化。基于狄拉克-弗伦克尔含时变分原理的运动方程是通过使用最近开发的 MPS 的切空间投影和投影分裂技术推导出来的。出现在 MCTDH 单粒子函数运动方程中的平均场算符，用 MPS 形式表示，并通过类似于密度矩阵重整化群扫的扫算算法进行高效评估。通过扩展激子分子系统的量子动力学模拟，证明了 MPS 逼近 MCTDH 的效率和收敛性。
