01304nas a2200133 4500008004100000245010100041210006900142260001400211520085700225100001701082700001901099700001501118856003701133 2021 eng d00aHyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations0 aHyperInvariant MERA Approximate Holographic Error Correction Cod c3/15/20213 a
We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.
1 aCao, ChunJun1 aPollack, Jason1 aWang, Yixu uhttps://arxiv.org/abs/2103.0863101494nas a2200181 4500008004100000245005100041210005100092260001500143300001100158490000700169520100800176100001401184700001701198700002501215700001901240700001601259856003701275 2020 eng d00aMore of the Bulk from Extremal Area Variations0 aMore of the Bulk from Extremal Area Variations c12/24/2020 a0470010 v383 aIt was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.
1 aBao, Ning1 aCao, ChunJun1 aFischetti, Sebastian1 aPollack, Jason1 aZhong, Yibo uhttps://arxiv.org/abs/2009.07850