Loschmidt amplitude spectrum in dynamical quantum phase transitions

Dynamical quantum phase transitions (DQPTs) are criticalities in the time evolution of systems and their existence has been theoretically predicted experimentally observed. However, how system behaves vicinity DQPT its connection to physical observables remains an open question. In this work, we introduce concept Loschmidt amplitude spectrum (LAS), which extends Loscmidt - detector transition by considering overlap initial state all eigenstates prequench Hamiltonian. By analyzing LAS integrable transverse-field Ising model, find that undergoes a population redistribution momentum space across DQPT. quasiparticle picture, collective excitations around lower-half $k$ modes become dominant when approaches The is also applicable study dynamics nonintegrable models where have investigated model with next-nearest-neighbor interactions as example. system's magnetization found be connected products there exists simultaneous time-evolved pairs prequnech Hamiltonian possess spin configurations negative magnetization. Our findings provide better understanding characteristics out-of-equilibrium