  Application of sufficiently strong electric fields to insulators induces
finite currents and then the insulators become metallic. This phenomenon is
called dielectric breakdown and known as a fundamental nonequilibrium and
nonlinear transport phenomenon in solids. Here, we study the dielectric
breakdown of generic strongly correlated insulators in one dimension. Combining
bosonization techniques with a theory of quantum tunneling, we develop an
effective field-theoretical description of dielectric breakdown with a
non-Hermitian sine-Gordon theory. Then, we derive an analytic formula of the
threshold field which is a many-body generalization of the Landau-Zener
formula. Importantly, we point out that the threshold field contains a
previously overlooked factor originating from charges of elementary
excitations, which should be significant when a system has fractionalized
excitations. We apply our results to integrable lattice models and confirm that
our formula is valid in a broad range including the weak coupling regime,
indicating its wide and potential applicability. Our results unveil universal
aspects in nonlinear and nonequilibrium transport phenomena for various
strongly correlated insulators.
