迈向显式离散全息术：来自双曲拼接的非周期自旋链
Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
摘要：
我们提出了一个新的例子，离散全息，提供了一个新的一步，建立离散空间的AdS/CFT对偶。一类边界哈密尔顿算子是从双曲庞加莱圆盘的规则平铺中以自然的方式获得的，通过一个膨胀规则，允许使用同心层的瓷砖来构建平铺。这类模型是非周期自旋链，其耦合序列由体膨胀规则得到。我们明确地选择非周期XXZ自旋链与自旋1/2自由度作为一个例子。利用强无序重整化群技术研究了该模型的性质，为该自旋链的基态提供了张量网络结构。这可以被视为离散体重构。此外，我们计算的纠缠熵在这种设置在两种不同的方式：一个离散化的Ryu-Takayanagi公式和推广的标准计算的边界非周期哈密顿量。对于这两种方法，对数增长的纠缠熵的子系统的大小被确定。系数，即有效中心荷，在两种情况下取决于体离散化参数，尽管以不同的方式。
英文摘要：
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic Poincaré disk, via an inflation rule that allows to construct the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains, whose sequences of couplings are obtained from the bulk inflation rule. We explicitly choose the aperiodic XXZ spin chain with spin 1/2 degrees of freedom as an example. The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. This can be regarded as discrete bulk reconstruction. Moreover we compute the entanglement entropy in this setup in two different ways: a discretization of the Ryu-Takayanagi formula and a generalization of the standard computation for the boundary aperiodic Hamiltonian. For both approaches, a logarithmic growth of the entanglement entropy in the subsystem size is identified. The coefficients, i.e. the effective central charges, depend on the bulk discretization parameters in both cases, albeit in a different way.
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