张量网络状态对应与全息
Tensor network state correspondence and holography
摘要：
近年来，张量网络态已经成为研究低能量子多体系统的一个非常有用的概念和模拟框架。在本文中，我们描述了一种特殊的方式，其中任何给定的张量网络可以被视为两个不同的量子多体状态的表示。这两个量子多体态通过张量网络相互对应。我们将这种“张量网络状态对应”--由于MERA是一个2D双曲张量网络（额外的维度被识别为1D系统的长度尺度），通过张量网络状态对应，从MERA获得的两个量子多体状态被认为是生活在离散双曲几何的边界上。从MERA得到的体态呈现出有趣的特征，其中一些特征讽刺了弦论全息对应的已知特征。我们展示了如何（i）散装状态承认的“全息屏幕”方面的描述，（ii）与一个关键的基态相关的共形场论数据可以从相应的散装状态，特别是，如何点状边界运营商被确定与扩展散装运营商。(iii)我们还提出了数值计算结果来说明，体态，双基态的几个关键的自旋链，具有指数衰减的相关性，和体相关长度一般随这些自旋链的中心荷的增加而减小。
英文摘要：
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"---a correspondence between quantum many-body states mediated by tensor networks as we describe---to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
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。
