Bulk-boundary correspondence from hyper-invariant tensor networks

TL;DR

This paper introduces a hyper-invariant tensor network model that simulates the AdS/CFT correspondence, accurately reproducing boundary correlation functions and elucidating bulk-boundary relations in holography.

Contribution

It presents a novel tensor network architecture that incorporates bulk indices to emulate holographic duality and recover key features like the HaPPY code's properties.

Findings

Successfully reproduces boundary two- and three-point correlation functions

Provides an efficient method for calculating correlation functions

Highlights the physical relation between bulk and boundary in tensor networks

Abstract

We introduce a tensor network designed to faithfully simulate the AdS/CFT correspondence, akin to the multi-scale entanglement renormalization ansatz (MERA), following hyper-invariant tensor network. The proposed construction integrates bulk indices within the network architecture to uphold the key features of the HaPPY code, including complementary recovery. This framework accurately reproduces the boundary conformal field theory's (CFT) two- and three-point correlation functions, while considering the image of any bulk operator. Furthermore, we provide an explicit methodology for calculating the correlation functions in an efficient manner. Our findings highlight the physical aspects of the relation between bulk and boundary within the tensor network models, contributing to the understanding and simulation of holographic principles in quantum information.