Nonarchimedean holographic entropy from networks of perfect tensors
Nonarchimedean holographic entropy from networks of perfect tensors
复制标题
DOI：
10.4310/atmp.2021.v25.n3.a2
复制
发表时间：
2018-12
影响因子：
1.5
通讯作者：
M. Heydeman;M. Marcolli;Sarthak Parikh;Ingmar Saberi
中科院分区：
文献类型：
--
作者：
M. Heydeman;M. Marcolli;Sarthak Parikh;Ingmar Saberi
我们考虑了一类全息量子纠错码，建立在网络配置双Bruhat-Tits树和它们的从属物由肖特基群对应的BTZ黑洞的完美张量。由此产生的全息态可以在无限网络尺寸的限制下构造。我们得到了一个p-adic版本的熵服从Ryu-Takayanagi一样的公式的二体纠缠的连接或断开的区域，在genus-zero和genus-one p-adic背景下，沿着与一个Bekenstein-Hawking-type公式的黑洞熵。我们证明了这样的张量网络，如次可加性，强次可加性，和一夫一妻的互信息（它总是饱和）服从熵不等式。此外，我们直接从有限域上相空间中的半经典态构造了无限类完美张量，推广了CRSS算法，并给出了表现为真空的哈密顿量。
We consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat-Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a p-adic version of entropy which obeys a Ryu-Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one p-adic backgrounds, along with a Bekenstein-Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semiclassical states in phase spaces over finite fields, generalizing the CRSS algorithm, and give Hamiltonians exhibiting these as vacua.