论文标题
临界量子动力学的数值模拟没有有限尺寸效应
Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects
论文作者
论文摘要
经典$（1+1）d $细胞自动机，例如Domany-Kinzel细胞自动机，是用于研究非平衡现象的范式系统。此类系统在离散的时间步长中演变，因此没有时间散布错误。此外，可以通过模拟初始种子的演变来获得有关临界现象的信息，该种子在任何有限的时间都只能在有限的轻锥上支撑。这基本上允许数值精确的模拟，没有有限尺寸的错误或边界效应。在这里，我们展示了如何在量子状态下获得类似的优势：从种子初始条件开始时，可以直接在无限晶格上直接在无限晶格上研究具有$（1+1）d $量子细胞自动机的多体临界动力学。通过使用张量网络模拟相关的一维，非单身量子细胞自动机的动力学，可以有效地实现这一点。我们将我们的方法应用于最近引入的模型，并找到通用指数的准确值，这表明这种方法可以是对量子系统中非平衡通用物理学进行精确分类的强大工具。
Classical $(1+1)D$ cellular automata, as for instance Domany-Kinzel cellular automata, are paradigmatic systems for the study of non-equilibrium phenomena. Such systems evolve in discrete time-steps, and are thus free of time-discretisation errors. Moreover, information about critical phenomena can be obtained by simulating the evolution of an initial seed that, at any finite time, has support only on a finite light-cone. This allows for essentially numerically exact simulations, free of finite-size errors or boundary effects. Here, we show how similar advantages can be gained in the quantum regime: The many-body critical dynamics occurring in $(1+1)D$ quantum cellular automata with an absorbing state can be studied directly on an infinite lattice when starting from seed initial conditions. This can be achieved efficiently by simulating the dynamics of an associated one-dimensional, non-unitary quantum cellular automaton using tensor networks. We apply our method to a model introduced recently and find accurate values for universal exponents, suggesting that this approach can be a powerful tool for precisely classifying non-equilibrium universal physics in quantum systems.
