Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion
Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion
复制标题
适当正则化 ML-MCTDH 运动方程的重要性
DOI：
10.1021/acs.jpca.0c11221
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Meyer, Hans-Dieter
中科院分区：
文献类型：
--
作者：
Wang, Haobin;Meyer, Hans-Dieter
当波函数展开式中存在虚拟轨道（未占据的单粒子函数）时，多配置瞬态哈特里 (MCTDH) 方法及其推广，多层 MCTDH (ML-MCTDH) 会产生奇异的运动方程 (EOM)。几十年来，这种奇点已经通过正则化约简密度矩阵在数值上被消除了。在本视角中，我们讨论了最近提出的对系数张量进行正则化的提议，这对 MCTDH 和 ML-MCTDH 中 EOM 解决挑战性问题的效率和正确性产生了重大影响。我们进一步证明，当系统变得很大以至于需要使用多层的 ML-MCTDH 时，采用这种新的正则化方案就变得更加重要。我们通过研究一个包含多达 100000 个模式的大浴的自旋玻色子模型来说明这一点。我们表明，即使在弱耦合状态下，也需要新的正则化方案才能将虚拟轨道快速旋转到希尔伯特空间中的正确方向。我们认为，将瞬态张量网络方法应用于任何足够大的系统时，这种情况可能很常见。
The multiconfiguration time-dependent Hartree (MCTDH) method and its generalization, the multilayer MCTDH (ML-MCTDH), result in equations of motion (EOMs) that are singular when there are virtual orbitals—the unoccupied single-particle functions—in the wave function expansion. For decades this singularity had been numerically removed by regularizing the reduced density matrix. In this Perspective we discuss our recent proposal to regularize the coefficient tensor instead, which has significant impact on both the efficiency and correctness of the EOMs in MCTDH and ML-MCTDH for challenging problems. We further demonstrate that when the system becomes large such that it is necessary to use ML-MCTDH with many layers, it is much more important to employ this new regularization scheme. We illustrate this point by studying a spin–boson model with a large bath that contains up to 100 000 modes. We show that even in the weak coupling regime the new regularization scheme is required to quickly rotate the virtual orbitals into the correct directions in Hilbert space. We argue that this situation can be common for applying a time-dependent tensor network approach to any large enough system.