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arXiv 2402.05910hep-thquant-ph
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背景无关的张量网络

Background independent tensor networks

Chris Akers, Annie Y. Wei

AI总结:

本文指出全息张量网络可构建为背景无关形式,消除背景纠缠以建模更大的码子空间,并讨论了相关细节及其与随机CFT数据的联系。

摘要:

传统的全息张量网络可以被描述为由许多在空间局部起作用的小线性映射构建的玩具全息映射,它们通过“背景纠缠”(即固定状态的链接,通常是最大纠缠态)连接在一起。然而,这些构建方法无法对真实的全息映射进行建模。原因之一是它们的“面积”是平庸的,对所有状态取相同的值,这与引力中几何是动力学的情况不同。最近,新的构建方法通过增加“存在于链接上”的自由度改善了这一问题。这使得面积变得非平庸,等于背景纠缠部分加上一个依赖于链接自由度状态的新正部分。尽管如此,这仍然存在背景纠缠的缺点,因此它只能对相对有限的码子空间进行建模,在这些子空间中,每个面积都有由背景纠缠给定的确定最小值。在本文中,我们仅指出这些构建方法的一个版本更进一步:它们可以是背景无关的,在全息映射中没有背景纠缠。这是有利的,因为它允许张量网络对更大的码子空间的全息映射进行建模。除了指出这一点,我们还讨论了使其生效所涉及的一些微妙之处,并指出了它与最近关于随机 CFT 数据讨论的绝佳联系。

英文摘要:

Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state, often the maximally entangled state. However, these constructions fall short of modeling real holographic maps. One reason is that their ``areas'' are trivial, taking the same value for all states, unlike in gravity where the geometry is dynamical. Recently, new constructions have ameliorated this issue by adding degrees of freedom that ``live on the links''. This makes areas non-trivial, equal to the background entanglement piece plus a new positive piece that depends on the state of the link degrees of freedom. Nevertheless, this still has the downside that there is background entanglement, and hence it only models relatively limited code subspaces in which every area has a definite minimum value given by the background entanglement. In this note, we simply point out that a version of these constructions goes one step further: they can be background independent, with no background entanglement in the holographic map. This is advantageous because it allows tensor networks to model holographic maps for larger code subspaces. In addition to pointing this out, we address some subtleties involved in making it work and point out a nice connection it offers to recent discussions of random CFT data.

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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