Theory of finite-size scaling in dynamical quantum phase transitions
Phys. Rev. A 112, 042203 – Published 1 October, 2025
DOI: https://doi.org/10.1103/9zwv-s4bn
Abstract
Dynamical quantum phase transitions (DQPTs) appear as nonanalyticities during the coherent evolution of closed systems. However, understanding the scaling behaviors in realistic finite-size systems is intricate and requires a framework beyond thermalized equilibrium analogies. We propose a general dynamical quantum finite-size scaling theory and demonstrate its validity using numerical and analytical approaches in a spin chain. Combining fidelity and renormalization group, we identify the scaling behavior of the transverse magnetization that simultaneously exhibits quantum coherence and statistical properties. In addition, we adapt generalized correlation functions in quantum chemistry protocols to visualize the effective light cone of quantum mutual information, demonstrating the importance of the coherence propagation to DQPTs. Our work provides a phenomenological insight and a quantitative analysis to the underlying microscopic entanglement evolution, offering an alternative interpretation of DQPTs and advancing the understanding of many-body physics.
