Determination of dynamical quantum phase transitions for boson systems using the Loschmidt cumulants method

We study the dynamical quantum phase transition (DQPT) of the Bose-Hubbard model utilizing the recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, which makes it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbard model is also investigated.