We introduce a class of quantum non-Markovian processes—dubbed process trees—that exhibit polynomially decaying temporal correlations and memory distributed across timescales. This class of processes is described by a tensor network with treelike geometry whose component tensors are (1) causality-preserving maps (superprocesses) and (2) locality-preserving temporal change-of-scale transformations. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects and can accommodate genuinely quantum power-law correlations in time. Importantly, this class allows efficient computation of multitime correlation functions. To showcase the potential utility of this model-agnostic class for numerical simulation of physical models, we show how it can efficiently approximate the strong memory dynamics of the paradigmatic spin-boson model, in terms of arbitrary multitime features. In contrast to an equivalently costly matrix-product-operator representation, the ansatz produces a fiducial characterization of the relevant physics. Finally, leveraging 2D tensor-network renormalization-group methods, we detail an algorithm for deriving a process tree from an underlying Hamiltonian via the Feynmann-Vernon influence functional. Our work lays the foundation for the development of more efficient numerical techniques in the field of strongly interacting open quantum systems, as well as the theoretical development of a temporal renormalization-group scheme. Published by the American Physical Society 2024

中文翻译：

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使用 Tree-Geometry Process Tensor 捕获长距离内存结构


我们介绍了一类量子非马尔可夫过程（称为过程树），它们表现出多项式衰减的时间相关性和跨时间尺度分布的记忆。这类过程由具有树状几何的张量网络描述，其组件张量是 （1） 因果关系保留映射（超级过程）和 （2） 局部保持时间尺度变化变换。我们表明，这类过程中的长程相关性往往几乎完全来自记忆效应，并且可以在时间上容纳真正的量子幂律相关性。重要的是，此类允许高效计算多时间相关函数。为了展示这个与模型无关的类在物理模型数值模拟中的潜在用途，我们展示了它如何有效地近似范式自旋玻色子模型的强内存动力学，即任意多时间特征。与同等昂贵的矩阵-乘积-运算符表示形式相反，拟设生成相关物理场的基准特征。最后，利用 2D 张量网络重整化组方法，我们详细介绍了一种通过 Feynmann-Vernon 影响泛函从底层哈密顿量派生过程树的算法。我们的工作为在强相互作用的开放量子系统领域开发更高效的数值技术以及时间重整化群方案的理论发展奠定了基础。 美国物理学会 2024 年出版