Coarse graining of spin net models: dynamics of intertwiners

TL;DR

This paper investigates simplified spin net models related to quantum gravity, using tensor network renormalization to analyze their phase diagram and discover a new fixed point with potential implications for continuum limits.

Contribution

It introduces a coarse graining method for spin net models and identifies a novel triangulation invariant fixed point, advancing understanding of quantum gravity models.

Findings

Determined the phase diagram of certain spin net models.

Discovered an unexpected fixed point defining a new vertex model.

Provided insights into continuum phases of quantum gravity analogues.

Abstract

Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four--dimensional models. We consider here simplified analogue models, so called spin nets, that retain the main dynamical ingredient of spin foams, the simplicity constraints. For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model.