# Integrability of a non-integrable quantum spin model at critical point

Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known? In the field of 2d classical models, the three-state Potts model is not in general integrable, but this model is integrable at the critical point.

• For instance, extended Bose Hubbard model is non-integrable, however, in the phase diagram, there exists a $c=1/2$ CFT, i.e. "integrable" as a CFT, as explained explicitly in this article, arxiv.org/abs/1812.03489 – Exhaustive May 28 at 15:34