Dynamical quantum phase transitions (DQPTs) feature singular temporal behavior in transient quantum states during nonequilibrium real-time evolution. In this work we show that DQPTs in random Ising chains exhibit critical behavior with nontrivial exponents that are not integer valued and not of mean-field type. By means of an exact renormalization group transformation we estimate the exponents with high accuracy eliminating largely any finite-size effects. We further discuss how the considered dynamical phenomena can be made accessible in current Rydberg atom platforms. In this context we explore signatures of the DQPTs in the statistics of spin configuration measurements available in such architectures. Specifically, we study the statistics of clusters of consecutively aligned spins and observe a marked influence of the DQPT on the corresponding distribution.

中文翻译：

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随机 Ising 链中动态量子相变的非常规临界指数

动态量子相变 (DQPT) 在非平衡实时演化期间的瞬态量子态中具有奇异的时间行为。在这项工作中，我们展示了随机 Ising 链中的 DQPT 表现出具有非整数值且非平均场类型的非平凡指数的关键行为。通过精确的重整化群变换，我们以高精度估计指数，在很大程度上消除了任何有限大小的影响。我们进一步讨论了如何在当前的里德堡原子平台中访问所考虑的动力学现象。在这种情况下，我们在此类体系结构中可用的自旋配置测量的统计数据中探索 DQPT 的特征。具体来说，