Li Weitang, Ren Jiajun, Yang Hengrui, Wang Haobin, Shuai Zhigang
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, People's Republic of China.
Tencent Quantum Lab, Tencent, Shenzhen 518057, People's Republic of China.
J Chem Phys. 2024 Aug 7;161(5). doi: 10.1063/5.0218773.
Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree method. In this work, we present an algorithm that automatically constructs the optimal and exact tree tensor network operators (TTNO) for any sum-of-product symbolic quantum operator. The construction is based on the minimum vertex cover of a bipartite graph. With the optimal TTNO, we simulate open quantum systems, such as spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions. In these simulations, the environment is treated as discrete modes and its wavefunction is evolved on equal footing with the system. We employ the Cole-Davidson spectral density to model the glassy phonon environment and incorporate temperature effects via thermo-field dynamics. Our results show that the computational cost scales linearly with the number of discretized modes, demonstrating the efficiency of our approach.
树张量网络态（TTNS）基于树拓扑结构将系统波函数分解为低秩张量的乘积，是多层多组态含时Hartree方法的基础。在这项工作中，我们提出了一种算法，该算法能为任何乘积和形式的符号量子算符自动构建最优且精确的树张量网络算符（TTNO）。这种构建基于二分图的最小顶点覆盖。利用最优TTNO，我们模拟了开放量子系统，比如自旋 - 玻色子模型中的自旋弛豫动力学以及分子结中的电荷传输。在这些模拟中，环境被视为离散模式，其波函数与系统在同等基础上进行演化。我们采用Cole - Davidson谱密度来模拟玻璃态声子环境，并通过热场动力学纳入温度效应。我们的结果表明，计算成本与离散模式的数量呈线性比例关系，证明了我们方法的有效性。
