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arXiv 1805.03071hep-thcond-mat.str-elgr-qcquant-ph
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关于张量网络因果结构的注记

Notes on the Causal Structure in a Tensor Network

Arpan Bhattacharyya, Long Cheng, Ling-Yan Hung, Sirui Ning, Zhi Yang

备注：
The typos are fixed, a shorter version with the new title "Emergent Lorentz symmetry and the Unruh effect in a Lorentzian Fermionic Tensor Network" has been published in PRD
发表信息：
Phys. Rev. D 99, 086007 (2019)
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摘要：

在本文中，我们试图了解洛伦兹张量网络，作为构建张量网络，可以描述更奇特的背景，如黑洞的准备。为了定义张量网络上的参考系和参考系转换的概念，我们将借用代数量子场论文献中的思想。有了这些定义，我们构造了洛伦兹张量网络的简单例子，并基于费米子的高斯模型和可积模型，解决了选择“惯性系”的谱。特别是，张量网络可以被看作是一个周期性驱动的Floquet系统，它绕过了“倍增问题”，并产生了具有精确线性色散关系的费米子。我们将发现，连接不同惯性系的助推算子和"林德勒双折射“的概念可以被定义，洛伦兹不变QFT中的重要物理，如昂鲁效应，可以被这样的时空骨架所捕获。当同样的方法直接应用于玻色子时，我们发现了有趣的微妙之处--算子代数包含了取错符号的算子--类似于视界后面的玻色子。

英文摘要：

In this paper we attempt to understand Lorentzian tensor networks, as a preparation for constructing tensor networks that can describe more exotic backgrounds such as black holes. To define notions of reference frames and switching of reference frames on a tensor network, we will borrow ideas from the algebraic quantum field theory literature. With these definitions, we construct simple examples of Lorentzian tensor networks and solve the spectrum for a choice of ``inertial frame'' based on Gaussian models of fermions and integrable models. In particular, the tensor network can be viewed as a periodically driven Floquet system, that by-pass the ``doubling problem'' and gives rise to fermions with exactly linear dispersion relations. We will find that a boost operator connecting different inertial frames, and notions of ``Rindler observers'' can be defined, and that important physics in Lorentz invariant QFT, such as the Unruh effect, can be captured by such skeleton of spacetime. We find interesting subtleties when the same approach is directly applied to bosons -- the operator algebra contains commutators that take the wrong sign -- resembling bosons behind horizons.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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