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

TL;DR

This paper explores a quantum generalization of the bit threads concept using MERA tensor networks, revealing how isometries act as sources of information flow and connecting entanglement properties to emergent classical gravity in the large central charge limit.

Contribution

It introduces a novel interpretation of MERA isometries as sources of information flow, extending the bit threads framework to quantum tensor networks and linking entanglement to emergent gravity.

Findings

Isometries in MERA act as sources or sinks of information flow.

The modified bit threads picture incorporates a density variable for isometries.

Entanglement entropy properties like strong subadditivity are derived in this framework.

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.