Integrability and chaos of 1+1d chiral edge states with Abelian anyons

1+1d chiral edge states with marginal interactions, which may arise on the edge of 2+1d topological phases, have rich quantum dynamics. In this talk, we first present a model consisting of $N$ interacting $SU(M)_1$ Wess-Zumino-Witten models hosting Abelian anyons, dubbed ``chiral Sachdev-Ye'' model. We analytically solve this model in two limits discovering behaviors from completely integrable to quantum chaos. We further extend our studies to the edge theory of a $\nu=4/3$ fractional quantum Hall state which show unusual integrability behavior.