  We propose a spinless Bose-Hubbard model in an one-dimensional (1D)
double-chain tilted lattice at unit filling per cell. A subspace of this model
can be faithfully mapped to the 1D transverse Ising model through superexchange
interaction with second-order perturbation theory. At a valid parameter region,
numerical results show good agreement of these two models both on energy
spectrums and correlation functions. And we show that the dynamical quantum
phase transition of the effective 1D transverse Ising model can be simulated.
With carefully designed procedures for producing the dynamical quantum phase
transition of the 1D transverse Ising model from a Mott insulator, the rate
function of the recurrence probability to the ground-state manifold shows the
same nonanalyticality at periodic time points as theory predicts. Our results
may give some inspirations on simulating 1D transverse Ising model with
superexchange interaction and exploring its dynamical quantum phase transition
in experiment.
