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arXiv:1001.0909 · The European Physical Journal B

Correlation properties of anisotropic XY model with a sudden quench

Haizhong Guo, Zhao Liu, Heng Fan, S. Chen

Published Feb 1, 2011• 4 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2011-10669-1

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We study the influence of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain after a sudden quench. The formulas to calculate the Loschmidt echo and Fisher zeros of the inhomogeneous XY chain are derived in real space. It is found that new DQPTs appear in the presence of weak disorder for the quenches across the Ising transition and two quantum phase transitions (Ising and anisotropic transitions). As the disorder strength increases, it's demonstrated that the Fisher zeros coalesce to regions on the imaginary axis in the thermodynamic limit. The DQPTs occur at the critical times corresponding to the boundaries of the Fisher zeros regions on the imaginary axis. However, for the quench across the anisotropic transition, the Fisher zeros regions appear even for the very weak disorder. Finally, for the quench within the same phase, the weak disorder is found having no effect on the DQPTs, but the DQPTs will be washed out in the presence of strong disorder.
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Previous investigations of dynamical quantum phase transition (DQPT) have predominantly focused on sudden quench protocols. In this work, we systematically explore the fate of DQPT from the sudden to the slow quench regime. We establish that DQPT remains robust under slow quenching when the protocol crosses an equilibrium quantum phase transition. Conversely, we show that accidental DQPTs,which occur when the pre and post quench Hamiltonians reside in the same equilibrium phase, can be filtered out in the slow quench limit. This demonstrates that slow quenches can reveal the intrinsic connection between DQPT and equilibrium quantum phase transitions, thereby enabling DQPT to serve as a dynamical probe for identifying equilibrium quantum critical points. We illustrate these findings with examples from the XY chain, the Aubry-André model, and the trimer Su-Schrieffer-Heeger model.