Quantum Breakdown Model and the Exponential U(1) Symmetry

Biao Lian presents a one-dimensional quantum breakdown model for bosons and spins with a U(1) charge that decreases exponentially across space. A transition separates a symmetric paramagnet from a condensate that breaks this symmetry. The condensate has no gapless Goldstone mode and therefore remains stable at zero temperature in one dimension. Its exponentially large ground-state degeneracy resembles a glass without requiring disorder, challenging established phase classifications.