论文标题
超跨随机自旋张量网络及其全息特性
Superposed Random Spin Tensor Networks and their Holographic Properties
论文作者
论文摘要
我们在一类旋转网络状态下研究边界到结合全息图的标准和性质，该旋转网络由类似于预测的纠缠对状态（PEPS）定义。特别是，我们考虑了与图形上定义明确的离散几何形状相对应的状态的叠加。通过应用随机张量平均技术，我们将熵计算映射到同一图上的随机ISING模型，并通过涉及几何形状的相对大小确定耦合的分布。此处使用的具有可变键化尺寸的张量网络的叠加呈现出在几何背景上的真实量子总和的图片。我们发现，每当每个几何形状产生固定边界区域C与其补体的等轴测映射时，他们的叠加就会这样，如果进入每个几何形状的相对重量与其大小成反比。此外，我们计算给定边界区域面积的平均值和方差，并发现平均值分别通过单个区域的平均值和总和从下和更高的角度进行。最后，我们对我们程序的可能扩展进行了展望，并突出了实施这些计划的概念限制。
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to well-defined, discrete geometries on a graph. By applying random tensor averaging techniques, we map entropy calculations to a random Ising model on the same graph, with distribution of couplings determined by the relative sizes of the involved geometries. The superposition of tensor network states with variable bond dimension used here presents a picture of a genuine quantum sum over geometric backgrounds. We find that, whenever each individual geometry produces an isometric mapping of a fixed boundary region C to its complement, then their superposition does so iff the relative weight going into each geometry is inversely proportional to its size. Additionally, we calculate average and variance of the area of the given boundary region and find that the average is bounded from below and above by the mean and sum of the individual areas, respectively. Finally, we give an outlook on possible extensions to our program and highlight conceptual limitations to implementing these.
