作为路径积分几何的张量网络
Tensor networks as path integral geometry
摘要：
在低能物理对应于共形场论（CFT）的量子临界自旋链的背景下，最近证明了[A.米尔斯特德湾Vidal，arXiv：1805.12524]，用于数值描述自旋链的基态的某些类别的张量网络也可以用于在晶格上实现（离散的近似版本）共形变换。在连续统中，相同的保角变换可以通过CFT路径积分在弯曲时空上实现。基于这一观察，在本文中，我们建议将张量网络本身解释为弯曲时空上的路径积分。这种观点赋予张量网络一个几何（一个离散的近似版本），即底层弯曲时空的几何。
英文摘要：
In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for numerically describing the ground state of the spin chain can also be used to implement (discrete, approximate versions of) conformal transformations on the lattice. In the continuum, the same conformal transformations can be implemented through a CFT path integral on some curved spacetime. Based on this observation, in this paper we propose to interpret the tensor networks themselves as a path integrals on curved spacetime. This perspective assigns (a discrete, approximate version of) a geometry to the tensor network, namely that of the underlying curved spacetime.
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