Influence of weak disorder on the dynamical quantum phase transitions in the anisotropic XY chain

We study the influence of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain after a sudden quench. The formulas to calculate the Loschmidt echo and Fisher zeros of the inhomogeneous XY chain are derived in real space. It is found that new DQPTs appear in the presence of weak disorder for the quenches across the Ising transition and two quantum phase transitions (Ising and anisotropic transitions). As the disorder strength increases, it's demonstrated that the Fisher zeros coalesce to regions on the imaginary axis in the thermodynamic limit. The DQPTs occur at the critical times corresponding to the boundaries of the Fisher zeros regions on the imaginary axis. However, for the quench across the anisotropic transition, the Fisher zeros regions appear even for the very weak disorder. Finally, for the quench within the same phase, the weak disorder is found having no effect on the DQPTs, but the DQPTs will be washed out in the presence of strong disorder.