Author(s): Yu-Min Hu, Zhaoyu Han, and Biao Lian We study the phase diagram of a one-dimensional spin quantum breakdown model, which has an exponential $U(1)$ symmetry with charge unit decaying as ${2}^{−j}$ with site position $j$. By exact diagonalization and density matrix renormalization group, we show that the model with spin $S≥2$ exhibits an… [Phys. Rev. Lett. 137, 096002] Published Thu Aug 27, 2026