Zeros of the Loschmidt amplitude in the quenched XY model
We investigate the notion of dynamical quantum phase transitions (DQPTs) in the quenched ground state of the spin-1/2 XY model H(h0, γ0) to H(h1, γ1). By a Wick rotation, the Loschmidt amplitude is formally treated as a canonical partition function and its zeros used as a probe for criticality. This approach is similar to that used in a Fisher zero analysis in identifying classical phase transitions. The occurrence of real-time zeros for the Loschmidt amplitude signify DQPTs. Previously, a correspondence between DQPTs and quenches across critical points was observed for the transverse-field Ising model. The zeros of the Loschmidt amplitude in a quench of the XY model ground state was calculated and the corresponding condition for a DPQT to occur was derived for a generic quench. It can be observed that not all quenches across critical points are accompanied by DQPTs and vice versa. This result is consistent with previous studies of the quenched XY model.