  The dynamical quantum phase transition is characterized by the emergence of
nonanalytic behaviors in the rate function, corresponding to the occurrence of
exact zero points of the Loschmidt echo in the thermodynamical limit. In
general, exact zeros of the Loschmidt echo are not accessible in a finite-size
quantum system except for some fine-tuned quench parameters. In this work, we
study the realization of the dynamical singularity of the rate function for
finite-size systems under the twist boundary condition, which can be introduced
by applying a magnetic flux. By tuning the magnetic flux, we illustrate that
exact zeros of the Loschmidt echo can be always achieved when the postquench
parameter is across the underlying equilibrium phase transition point, and thus
the rate function of a finite-size system is divergent at a series of critical
times. We demonstrate our theoretical scheme by calculating the
Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its
applicability to more general cases. Our result unveils that the emergence of
dynamical singularity in the rate function can be viewed as a signature for
detecting dynamical quantum phase transition in finite-size systems. We also
unveil that the critical times in our theoretical scheme are independent on the
systems size, and thus it provides a convenient way to determine the critical
times by tuning the magnetic flux to achieve the dynamical singularity of the
rate function.
