Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

中文翻译：

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有限温度下两浴自旋玻色子模型中非平衡稳态和瞬态热流的矩阵积态模拟


模拟开放量子系统的非微扰和非马尔可夫动力学是一个非常具有挑战性的多体问题，因为需要在平等的基础上进化系统及其环境。张量网络和矩阵积态（MPS）已成为开放系统模型的强大工具，但处理有限温度环境所需的数值资源增长极其迅速，限制了它们的应用。在本研究中，我们使用 MPS 的时间相关变分演化来探索 Tamascelli 等人的惊人理论。 （Phys. Rev. Lett. 2019, 123, 090402.）展示了如何从零温度（即纯波函数）模拟获得有限温度开放动力学。使用这种方法，我们为欧姆自旋玻色子模型的动力学在广泛的耦合强度和温度范围内生成了基准数据集，并且还对模拟非平衡稳态的数值成本进行了详细分析，例如来自量子位与不同温度的浴的非微扰耦合。尽管资源需求不断增长，我们发现可以获得收敛的非微扰结果，并且我们讨论了许多最新的想法和数值技术，这些想法和数值技术应该允许 MPS 广泛应用于复杂的开放量子系统。