Dynamical Quantum Phase Transitions in the 1D Nonintegrable Spin‐1/2 Transverse Field XZZ Model

Using the Jordan–Wigner mean‐field (JW‐MF) approach, the dynamical quantum phase transition (DQPT) in the 1D spin‐1/2 XZZ model is studied, where the presence of the transverse magnetic field breaks the U(1) symmetry of the Hamiltonian and leads to loss of integrability. In the time evolution of the rate function, three kinds of behaviors will emerge: regular and irregular nonanalytic, and also regular analytic. Examples are given where the rate function shows the regular analytic can appear albeit a quench is crossed from a quantum critical point (QCP) and examples where the irregular nonanalyticity behaviors can arise in both quenching into the same phase and exceeded from a QCP. All the regular nonanalyticity behaviors at periodic instants t∗ happen when quenches cross from a QCP. In order to achieve a confirmation on our results, the long‐time average of the rate function is determined and show the occurrence of the nonequilibrium quantum phase transitions exactly at the QCPs and hence disclose the JW‐MF approach qualitatively works very well. The image shows a phase diagram of the 1D spin‐1/2 XZZ model in a transverse magnetic field: equilibrium (the red lines) versus nonequilibrium (the blue points). The latter case comes from the long‐time average of the rate function driven from the dynamical quantum phase transitions. Both extract from the Jordan–Wigner mean‐field approach. Surprisingly, there is a good agreement in both.