Central to the new frontiers of many-particle quantum physics is the time evolution of entanglement. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. We report a counterintuitive fundamental result in the dynamics of quantum entanglement that connects two seemingly unrelated fields, mesoscopic fluctuations in electronic systems and entanglement dynamics.
The underpinning of such phenomenon is an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable --- either free fermions or interacting spins --- lattice models. For each class, it leads to a universal scaling law for the variance in the long-time statistics of entanglement evolution, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes.
Our results have practical implications for controlling entanglement in mesoscopic devices and lay a theoretical foundation for understanding fluctuations observed in experiments using various quantum simulation platforms.
[1] Lih-King Lim, Cunzhong Lou, Chushun Tian, arXiv:2305.09962 (2023).
