



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<p>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.</p>1 aCao, ChunJun1 aPollack, Jason1 aWang, Yixu  uhttps://arxiv.org/abs/2103.0863101431nas a2200133   4500008004100000245007400041210006900115260001500184520099900199100001701198700002601215700001901241856003701260       2019                        eng d00aHow Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?0 aHow Low Can Vacuum Energy Go When Your Fields Are FiniteDimensio  c05/11/20193 a<p>According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this essay, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein-Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.</p>1 aCao, ChunJun1 aChatwin-Davies, Aidan1 aSingh, Ashmeet  uhttps://arxiv.org/abs/1905.11199