Quantum Mechanics and the Continuum Limit of an Emergent Geometry

TL;DR

This paper explores emergent spacetime models based on Ising spins, analyzing the dynamics of excitations and edge states, and suggests a possible Lieb-Robinson bound indicating a causal structure in these models.

Contribution

It provides a detailed analysis of excitation dynamics, including edge states, and proposes a numerical approach to estimate bounds on propagation speed in emergent geometry models.

Findings

Edge states influence excitation dynamics

Numerical bounds suggest a Lieb-Robinson limit

Potential for causal structure in emergent spacetime

Abstract

Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable excitations possessing many of the characteristics of a quantum particle. We analyze the dynamics of such excitations, including a detailed treatment of the edge states not previously addressed. Using a minimal prescription for the interaction of defects we numerically investigate approximate bounds to the speed of propagation of such a `particle'. We discover, using numerical simulations, that there may be a Lieb-Robinson bound to propagation that could point the way to how a causal structure could be accommodated in this class of emergent geometry models.