Information propagation in a non-local model with emergent locality

TL;DR

This paper investigates a non-local model where locality emerges from entanglement, revealing that hierarchy in interactions influences light-cone structures and can serve as a signature of emergent locality.

Contribution

It demonstrates how hierarchies in non-local interactions lead to layered light-cones, providing insights into emergent locality distinct from traditional local models.

Findings

Hierarchy of interactions creates layered light-cones.

Suppressed long-range interactions lead to linear, local-like light-cones.

Potential physical indicator for emergent locality in non-local systems.

Abstract

In this paper, we revisit a "relatively local" model proposed in arXiv:1811.07241, where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly velocity/ entanglement speed can be defined similarly, at least in the regime where locality is well defined and a light cone structure emerges in the correlation between sites. We find that the relations observed between them in local models arXiv:1908.06993 are not respected. In particular, we conjecture that the hierarchy of the interaction over different distances provides different "layers" of light-cones. When long range interactions are sufficiently suppressed, the effective light cones are dominated by linear behaviors with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models.