LAUSR

Abstract In this paper, we revisit a “relatively local” model proposed in [1], 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 [2] 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 behaviour with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models.