论文标题
有限尺寸量子系统中淬火动力学的速率函数的动力奇异性
Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems
论文作者
论文摘要
动力学量子相变的特征是速率函数中未分析行为的出现，对应于热力学极限中洛斯米特回声的精确零点。通常，除了一些微调的淬灭参数外，在有限大小的量子系统中无法访问Loschmidt Echo的精确零。在这项工作中，我们研究了有限大小系统在扭曲边界条件下的速率函数的动力学奇点的实现，这可以通过施加磁通量来引入。通过调谐磁通量，我们说明当Quechmidt Echo的精确零可以始终达到Quince posecter跨基础平衡相变点时，并且有限大小的系统的速率函数在一系列关键时段存在分歧。我们通过详细计算Su-Schrieffer-Heeger模型和Creutz模型来证明我们的理论方案，并在更一般的情况下展示其适用性。我们的结果揭示了速率函数中动态奇点的出现可以被视为用于检测有限大小系统中动态量子相变的签名。我们还揭示了我们的理论方案中的关键时期在系统大小上是独立的，因此，它通过调整磁通量以实现速率函数的动力学奇点来确定关键时期的方便方法。
The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.
