Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations
Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations
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DOI：
10.1021/acs.jctc.2c00209
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发表时间：
2022-06-14
影响因子：
5.5
通讯作者：
Batista, Victor S.
中科院分区：
文献类型：
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作者：
Lyu, Ningyi;Soley, Micheline B.;Batista, Victor S.
量子反应动力学的数值精确模拟，包括激发电子态的非绝热效应，对于获得超快化学反应性的基本见解和分子光谱的严格解释是必不可少的。在这里，我们介绍了张量列分裂算子KSL（TT-SOKSL）方法在张量列（TT）/矩阵乘积态（MPS）表示的量子模拟。TT-SOKSL使用时间演化算符的Trotter展开将量子态作为张量序列进行传播，就像张量序列分裂算符傅立叶变换（TT-SOFT）方法一样。然而，Trotter展开的指数算子是使用秩自适应TT-KSL方案来应用的，而不是像TT-SOFT中那样使用缩放和平方方法。我们证明了TT-SOKSL的准确性和效率，适用于模拟的视紫红质中的视网膜发色团的光致异构化，包括非绝热动力学势能面的圆锥形交叉点。量子演化是在全维中描述的一个依赖于时间的波包根据两个状态的25维模型哈密尔顿。我们发现，TT-SOKSL收敛速度比TT-SOFT张量列车表示的最大允许的内存要求，更好地保持规范的时间演变的状态。与基于TT-KSL方法的相应模拟相比，TT-SOKSL的优点是通过利用多维张量列傅立叶变换的线性缩放来避免构造矩阵乘积状态拉普拉斯算子。
Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.