SCIENCE SPIN-OFFS

[dockzef]

Tensor Network Theory - Part 1: Overview of core library and tensor operations

Sarah Al-Assam, Stephen R. Clark, Dieter Jaksch
(Submitted on 7 Oct 2016)

In this technical paper we introduce the Tensor Network Theory (TNT) library - an open-source software project aimed at developing robust, easy to use and highly optimised code for TNT calculations, available at this http URL The aims of this paper are threefold: to (i) give a brief but broad introduction to TNT, (ii) give an overview of the structure of TNT library, and (iii) describe in detail the core tensor features of the library.


https://arxiv.org/abs/1610.02244

;x;xxxxx;xxxxx xxxx44xdx
Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy

Muxin Han, Ling-Yan Hung
Comments: 26+1 pages, 5 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)

The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space S with boundary ?S is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region A and its complement A¯ are specified on the boundary ?S, we show that the boundary entanglement entropy S(A) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. S(A) is proportional to the minimal area of the bulk surface attached to the boundary of A in ?S.

https://arxiv.org/abs/1610.02134