Entanglement and universal dynamics in many-body localized systems

Wen Wei Ho, Dmitry A. Abanin

The dynamics of entanglement has recently been realized as a useful probe in studying ergodicity and its breakdown in quantum many-body systems. In this paper, we study theoretically the growth of entanglement in quantum many-body systems and propose a method to measure it experimentally. We show that entanglement growth is related to the spreading of local operators in real space. We present a simple toy model for ergodic systems in which linear spreading of operators results in a universal, linear-in-time growth of entanglement for initial product states, in contrast with the logarithmic growth of entanglement in many-body localized (MBL) systems. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of several copies of the original system, in which connections are controlled by a quantum switch (two-level system). By measuring only the switch's dynamics, the growth of the R\'enyi entropies can be extracted. Our work provides a way of understanding entanglement dynamics in many-body systems and to directly measure its growth in time via a single local measurement.

Jens Hjorleifur Bardarson

Robert Schittko, Alexander Lukin, Matthew Rispoli +6 more

Takahiro Orito, Yoshihito Kuno, Ikuo Ichinose

We study a canonical many-body-localized (MBL) system with power-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magnetic field. The power-law-correlated disorder can control the critical regime between the MBL and thermal (ergodic) phases by varying its exponent, and it let us investigate the MBL transitions in detail. Static-eigenstate and dynamic properties of MBL are studied by numerical methods for systems with various long-range correlations. By using energy-resolved distribution of the participation ratio (PR) and calculating some physical quantities related to localization length, we show that the MBL transition exhibits certain universal behavior. We also investigate entanglement properties for the static and dynamics system. These studies elucidate the impact of power-law-correlated disorders in the canonical MBL system.

J. W. Clark, Hessam Habibian, Aikaterini Mandilara +1 more

Chunyue Zhang, Zixiang Li, Shi‐Xin Zhang

Studies of entanglement dynamics in quantum many-body systems have focused largely on initial product states. Here, we investigate the far richer dynamics from initial entangled states, uncovering universal patterns across diverse systems ranging from many-body localization (MBL) to random quantum circuits. Our central finding is that the growth of entanglement entropy can exhibit a counterintuitive nonmonotonic dependence on the initial entanglement in many nonergodic systems, peaking for moderately entangled initial states. To understand this phenomenon, we introduce a conceptual framework that decomposes entanglement growth into two mechanisms: "build" and "move." The "build" mechanism creates new entanglement, while the "move" mechanism redistributes preexisting entanglement throughout the system. Specifically, we demonstrate that MBL dynamics are "move-dominated," exhibiting a quantitative agreement with a random SWAP circuit that serves as a model of pure "move" dynamics by uniformly distributing preexisting entanglement. This implies that MBL acts as a redistributor of a hidden entanglement reservoir quantified by the bipartition-averaged entropy. This "build-move" framework offers a unified perspective for classifying diverse physical dynamics, deepening our understanding of entanglement propagation and information processing in quantum many-body systems.