2016/10/31 by Muxin Han, Ling-Yan Hung · 1 citation
Physics and Astronomy · #cond-mat.str-el #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.95.024011
published as Phys. Rev. D 95, 024011 (2017) · 26+1 pages, 6 figures, reference added
arxiv created 2017/01/20 · arxiv updated 2017/01/24
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 Σ with boundary ∂Σ 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 ∂Σ, 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 ∂Σ.