Self-assembling tensor networks and holography in disordered spin chains
Self-assembling tensor networks and holography in disordered spin chains
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DOI：
10.1103/physrevb.89.214203
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发表时间：
2014-01
影响因子：
3.7
通讯作者：
A. M. Goldsborough;R. A. Romer
中科院分区：
文献类型：
--
作者：
A. M. Goldsborough;R. A. Romer
我们证明了 Hikihara 等人的数值强无序重整化群算法。 [物理。 Rev. B 60, 12116 (1999)] 一维无序海森堡模型自然地描述了具有由耦合强度定义的不规则结构的树张量网络 (TTN)。利用希尔伯特空间中 TTN 的全息解释，我们利用 TTN 的几何特性计算期望值、相关函数和纠缠熵。我们发现无序平均自旋相关性与通过张量网络的平均路径长度成比例，而纠缠熵则与连接两个区域的最小表面成比例。此外，纠缠熵随着无序度和系统尺寸的增加而增加，导致违反面积定律。我们的结果证明了自组装 TTN 方法对无序系统的有用性，并定量验证了全息术和量子多体系统之间的联系。
We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.