Stable excitations and holographic transportation in tensor networks of critical spin chains

TL;DR

This paper investigates the stability of holographic excitations in tensor network models of critical spin chains, revealing unstable hologrons and proposing stable boundary excitations that demonstrate holographic transportation observable in experiments.

Contribution

It demonstrates the instability of hologrons in tensor network models and introduces boundary excitations exhibiting holographic transportation, linking theoretical predictions with experimental observability.

Findings

Hologrons are unstable during dynamic evolution.

Stable bulk excitations can be constructed from boundary primary operators.

Boundary excitations exhibit observable holographic transportation.

Abstract

The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.