Holography and criticality in matchgate tensor networks

TL;DR

This paper develops a versatile tensor network framework to model holographic dualities, demonstrating critical Ising states on various bulk geometries and linking tensor networks with holographic quantum error correction.

Contribution

It introduces an efficient framework for Gaussian matchgate tensor networks, enabling the realization of critical boundary states on different bulk geometries and connecting holography with quantum error correction.

Findings

Realized critical Ising models on flat and hyperbolic lattices

Produced translation-invariant critical states with MERA-like tensor networks

Linked holographic quantum error correcting codes with tensor network models

Abstract

The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand such bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1+1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multi-scale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor-network models capturing bulk-boundary correspondences.