AI 中文总结
该研究提出涌现的副本时钟作为单一序参量，统一区分多体局域化与热化，其关联函数具三种渐近行为，可区分空间关联长度相同的局域化动力学。
AI 中文摘要
多体局域化（MBL）与本征态热化假设（ETH）传统上通过一系列独立的诊断方法区分，而非单一序参量。研究表明，孤立幺正动力学的复制与折叠会产生正向-反向历史配对的复杂统计力学，在闭合循环红外区域内，形成一个涌现的时钟$r_x\in\mathbb Z_t$。其关联函数具有三种不同的渐近行为：多体局域化（MBL）中呈指数衰减、临界点处呈无标度衰减、热化相中呈长程锁定。受控$l$比特约化使时钟作用量为准局域，其逆关联长度满足$\xi_{\rm pair}^{-1}=\kappa_{\rm el}=\ln|\rho_0/\rho_q|$，统一了历史相干性、缺陷线张力与转移谱。副本序提供了第二个离散坐标——首个可观测隐藏动力学不变量的阶——能够区分空间关联长度相同的局域化动力学。
英文摘要
Many-body localization (MBL) and eigenstate thermalization (ETH) are traditionally distinguished by a collection of separate diagnostics, not by a single order parameter. We show that replication and folding of isolated unitary dynamics generate a complex statistical mechanics of forward--backward history pairings and, in a closed cyclic infrared sector, an emergent clock $r_x\in\mathbb Z_t$. Its correlator has three distinct asymptotics: exponential decay in MBL, scale-free decay at criticality, and long-range locking in the thermal phase. A controlled $l$-bit reduction makes the clock action quasi-local, while its inverse correlation length obeys $ξ_{\rm pair}^{-1}=κ_{\rm el}=\ln|ρ_0/ρ_q|$, unifying history coherence, the defect line tension, and the transfer spectrum. Replica order supplies a second, discrete coordinate---the first order at which a hidden dynamical invariant becomes visible---and can distinguish localized dynamics that share the same spatial correlation length.
Comments5 pages, 3 figures
