Bosonic quantum breakdown Hubbard model

We propose a bosonic quantum breakdown Hubbard model, which generalizes the Bose-Hubbard model by adding an asymmetric breakdown interaction turning one boson into two between adjacent sites. When the normal hopping is zero, this model has a global exponential U(1) symmetry, and we show that the ground state undergoes a first-order phase transition from a Mott insulator (MI) to a spontaneously symmetry breaking (SSB) breakdown condensate as the breakdown interaction increases. Surprisingly, the SSB breakdown condensate does not have a gapless Goldstone mode, which invalidates theMermin-Wagner theorem and leads to stable SSB in one dimension. Moreover, we show that the quench dynamics of a boson added to MI exhibits a dynamical transition from dielectric to breakdown phases, which happens at a larger breakdown interaction than the groundstate phase transition. Between these two transitions, the MI (dielectric) state is a false vacuum stable against dynamical breakdown. Our results reveal that quantum models with unconventional symmetries such as the exponential symmetry can exhibit unexpected properties.