矩阵乘积态单点含时变分原理方法中键维的动态演化：非平衡开放量子动力学的有效模拟
Dynamically Evolving Bond-Dimensions within the one-site Time-Dependent-Variational-Principle method for Matrix Product States: Towards efficient simulation of non-equilibrium open quantum dynamics
摘要：
理解非马尔可夫和非微扰开放系统中涌现的系统浴相关性是一个理论挑战，它极大地受益于矩阵乘积状态（MPS）方法的应用。在这里，我们提出了一个自动适应的变体的单网站的时间相关的变分原理（1TDVP）方法的多体MPS波函数中，当地的键尺寸可以演变捕获不断增长的纠缠“在飞”。我们通过有效地检查在每个动态时间步之前增加每个MPS键维度的效果来实现这一点，从而导致MPS可以随着动态的复杂性在时间和空间上的增长而动态地和不均匀地重组自身。这自然会导致更有效的模拟，避免需要多次收敛运行，并且，正如我们所证明的，非常适合于描述连接到多个环境的开放量子系统的典型的有限温度“杂质”问题。
英文摘要：
Understanding the emergent system-bath correlations in non-Markovian and non-perturbative open systems is a theoretical challenge that has benefited greatly from the application of Matrix Product State (MPS) methods. Here, we propose an autonmously adapative variant of the one-site Time-Dependent-Variational-Principle (1TDVP) method for many-body MPS wave-functions in which the local bond-dimensions can evolve to capture growing entanglement 'on the fly'. We achieve this by efficiently examining the effect of increasing each MPS bond-dimension in advance of each dynamic timestep, resulting in an MPS that can dynamically and inhomogeneously restructure itself as the complexity of the dynamics grows across time and space. This naturally leads to more efficient simulations, oviates the need for multiple convergence runs, and, as we demonstrate, is ideally suited to the typical, finite-temperature 'impurity' problems that describe open quantum system connected to multiple environments.
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