  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. We show that the ground state undergoes
a first-order phase transition from Mott insulator to breakdown condensate as
the breakdown interaction increases. When the normal hopping is zero, this
model has a global exponential U(1) symmetry, which is spontaneously broken by
the breakdown condensate, while the Mott-condensate transition remains first
order. Surprisingly, the breakdown condensate with spontaneously broken
exponential U(1) symmetry does not have a gapless Goldstone mode, which
invalidates the Mermin-Wagner theorem and leads to stable spontaneous symmetry
breaking in 1D. Moreover, we show that the model at non-equilibrium exhibits a
dynamical transition from dielectric phase to breakdown phase with respect to
the breakdown interaction. Our results show that quantum systems with
exponential symmetry can exhibit novel unexpected properties.
