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量子多体伤痕态的弱遍历性动力学与本征态热化假说相悖,在淬火动力学中局域可观测量出现周期振荡.这种现象通常与伤痕态二分纠缠熵的亚体积定律有关.纠缠熵呈现出异常值,与能谱主体相分离.本文使用精确对角化的方法数值模拟了准一维分形子模型中的彩虹伤痕态,该态由一系列远距离的四体纠缠组成,依次分布于中心对称的四个格点,其二分纠缠熵遵循体积定律.我们发现该态在未与能谱主体分离的情况下,表现出了弱热化现象.当引入横场破坏模型的子系统对称性后,弱热化特性随即消失.进一步地,本文在分形子模型中提出了彩虹伤痕态的制备方案,通过调制局域的四体交换相互作用和 $\hat{\sigma}^z$ 门,从尼尔态出发,实现了高保真度的态制备.分析相互作用的强度噪声影响,该方案表现出一定的鲁棒性.本文证明了分形子模型中彩虹伤痕态的存在,为非平衡量子系统中弱热化的研究提供了新的途径.The eigenstate thermalization hypothesis describes the nonequilibrium dynamics of an isolated quantum many-body system, during which a pure state becomes locally indistinguishable from a thermal ensemble. The discovery of quantum many-body scars (QMBS) shows a weak violation of ergodicity, characterized by coherent oscillations of local observables after a quantum quench. These states consist of the tower of regular eigenstates which are equally spaced in the energy spectrum. While subextensive entanglement scaling is a primary feature widely used to detect QMBS numerically as entropy outliers, rainbow scars exhibit a volume-law scaling, which may challenge this property. In this work, we construct the rainbow scar state in the fracton model on a two-leg ladder. The fracton model is composed of four-body ring-exchange interactions and hosts global time-reversal symmetry $\hat{\mathcal{T}}=\mathcal{K} i \hat{\sigma}^y$ and subsystem $\mathrm{U}(1)=\prod_{j \in\{\mathrm{row} / \mathrm{col}\}} e^{i \frac{\theta}{2} \hat{\sigma}_j^z}$ symmetry. The subsystem symmetry constrains particle mobility, hindering the establishment of thermal equilibrium and leading to a series of anomalous dynamical processes. We construct the rainbow scar state with distributed four-body GHZ states whose entanglement entropy follows the volume law. By calculating the eigenstates of the fracton model with exact diagonalization, the rainbow scar state consists of a series of degenerate high-energy excited states, which are not clearly outliers among other eigenstates in the spectrum. Introducing the on-site interaction to break the time-reversal symmetry, the degeneracy of rainbow scar states is lifted into an equally spaced tower of states, ensuring the revivals of the initial states. However, when subsystem U(1) symmetry is broken, the scar state is quickly thermalized, indicating that weak thermalization may be protected by subsystem U(1) symmetry. Additionally, we propose a scheme for preparing the rainbow scar state by modulating the strength of the four-body interactions and $\hat{\sigma}^z$ operations, analyzing the impact of noise on the strength of the four-body interactions. This work provides new insights for the study of weak thermalization processes in fracton model and helps to understand the nature of ETH-violation in different nonequilibrium systems.
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