Quantum group spin nets: refinement limit and relation to spin foams

Understand

So far spin foam models are hardly understood beyond a few of their basic building blocks.

• To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their effective continuum dynamics via tensor network renormalization.
• In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the $BF$ phase.
• In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization.