用于求解运动层级方程的树张量网络态方法
Tree tensor network state approach for solving hierarchical equations of motion
AI总结：
针对开放量子系统动力学的HEOM方法，提出用树张量网络态表示扩展波函数并结合含时变分原理传播，在保证精度的同时将计算速度提升数个数量级，且优于一维矩阵乘积态方案。
摘要：
运动层级方程（HEOM）方法是一种数值精确的开放量子系统动力学方法。该方法以浴关联函数的指数展开为基础，本质上是将连续环境策略性地重塑为一组有效浴模式，从而在有限温度下实现更高效的截断。基于这一认识，可将HEOM方法映射为一类含非厄米超哈密顿量的类薛定谔方程，其扩展波函数是中心系统波函数与这些有效浴模式的福克态的张量积。\n认识到系统与这些有效浴模式形成星形纠缠结构，本研究探索了将扩展波函数表示为高效树张量网络态（TTNS）、将超哈密顿量表示为同结构树张量网络算符的可行性，并应用含时变分原理的时间传播算法开展计算。\n我们基于含慢弛豫浴的自旋玻色子模型进行了基准测试，结果表明，所提出的HEOM+TTNS方法与传统HEOM方法的计算结果一致，同时计算速度提升了数个数量级。此外，采用纯正TTNS的模拟比一维矩阵乘积态分解方案快4倍。
英文摘要：
The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a continuous environment into a set of effective bath modes that allow for more efficient cutoff at finite temperatures. Based on this understanding, one can map the HEOM method into a Schrödinger-like equation with a non-Hermitian super Hamiltonian for an extended wavefunction being the tensor product of the central system wave function and the Fock state of these effective bath modes. Recognizing that the system and these effective bath modes form a star-shaped entanglement structure, in this work, we explore the possibility of representing the extended wave function as an efficient tree tensor network state (TTNS), the super Hamiltonian as a tree tensor network operator of the same structure, as well as the application of a time propagation algorithm using the time-dependent variational principle. Our benchmark calculations based on the spin-boson model with a slow-relaxing bath show that, the proposed HEOM+TTNS approach yields consistent results with that of the conventional HEOM method, while the computation is considerably sped up by a factor of a few orders of magnitude. Besides, the simulation with a genuine TTNS is four times faster than a one-dimensional matrix product state decomposition scheme.
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