Quantum bit threads of MERA tensor network in large $c$ limit

Abstract

The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in understanding holography. In this paper, we investigate a quantum generalization of the "bit threads" based on tensor network, with particular interests in the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large $c$ limit, isometries of the MERA can be regarded as "sources" (or "sinks") of the information flow, which extensively modifies the original picture of the bit threads by introducing a new variable $\rho$: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large $c$ limit implies the classical gravity can be emerged from the information flow.