Dynamical quantum phase transitions in Stark quantum spin chains

We investigate the nonequilibrium dynamics of one-dimension spin models in the presence of uniform force. The linear potential induces a delocalization-localization transition in the free particle model, also known as the Wannier-Stark effect. We study dynamical quantum phase transition (DQPT) due to sudden global quenches across a quantum critical point when the system undergoes a localization-delocalization transition. In this regard, we consider the XX and XXZ spin chains and explore two types of quenches with and without crossing through the delocalization-localization point. The XX model was mapped to free fermion particles, so both analytical and numerical results were provided. Results reveal that the dynamical signature of localization- delocalization transitions can be characterized by nonanalyticities in dynamical free energy (corresponding to the zero points in the Loschmidt echo). We also explore interaction effects considering XXZ spin chains, using the time-dependent extension of the numerical DMRG technique. Our results show that depending on the anisotropic parameter increment & LGT; 1.0, if both the initial and post-quench Hamiltonians are in the same phase or not, DQPTs may happen. Moreover, the interrelation between DQPTs and different correlation measures such as the equilibrium order parameters or entanglement entropy production of the system remains unclear. We provide more analyses of the features of DQPTs, in both types of quenches, by connecting them to average local magnetization, entanglement entropy production, and the Schmidt gap.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

We investigated the dynamics of one-dimensional spin models with uniform force, observing delocalization-localization transitions induced by a linear potential. The study focused on the dynamical quantum phase transition (DQPT) during sudden global quenches across a quantum critical point. XX and XXZ spin chains were considered, with analysis and numerical results provided for the XX model, which was mapped to free fermion particles. Nonanalyticities in dynamical free energy were found to characterize the localization-delocalization transitions. Interaction effects were explored using the time-dependent DMRG technique for the XXZ spin chains. Results showed the occurrence of DQPTs depending on the anisotropic parameter increment. The relation between DQPTs and correlation measures such as equilibrium order parameters and entanglement entropy production remains unclear. Further analysis connected DQPTs to average local magnetization, entanglement entropy production, and the Schmidt gap. ©2023 Elsevier B.V. All rights reserved.