Floquet系统中具有离散时间晶体动力学的猫疤痕解析理论
Analytical theory of cat scars with discrete time crystalline dynamics in Floquet systems
AI总结：
本文重构谱配对理论，证明强Ising相互作用能稳定具有可调模式的“猫疤痕”本征态并引发局部离散时间晶体动力学，同时提出了表征其振幅、局域化和寿命的解析标度关系。
摘要：
我们重构了谱配对（SP）理论，以在不需预热化条件下对平移不变系统中的本征态时空序进行解析描述。研究表明，仅凭强Ising相互作用和驱动即可稳定一类具有可调模式的“猫疤痕”本征态，从而引发局部的离散时间晶体（DTC）动力学。它们表现出Fock空间局域化和长程关联，在无序自由场景下对一般扰动具有鲁棒性。特别地，我们引入了一种对称性指标方法来枚举猫疤痕，借此除了先前发现的铁磁疤痕外，还识别出一系列意想不到的非均匀疤痕模式。这些疤痕强制产生具有刚性非均匀模式的DTC动力学，为在实验上验证潜在的本征态性质提供了可行途径。此外，我们严格证明了强Ising相互作用对不同阶扰动施加了选择规则，从而对Floquet本征态的自旋涨落产生指数级抑制。基于这一性质，证明了三个解析标度关系，用于表征与猫疤痕相关的DTC动力学的振幅、Fock空间局域化和寿命。我们进一步提供了两种实用方法，以检验特定DTC现象是由单自旋动力学主导，还是源于真正的相互作用效应。
英文摘要：
We reconstruct the spectral pairing (SP) theories to enable analytical descriptions of eigenstate spatiotemporal orders in translation-invariant systems without prethermal conditions. It is shown that the strong Ising interactions and drivings alone stabilize a class of ``cat scar" eigenstates with tunable patterns, which lead to {\em local} discrete time crystal (DTC) dynamics. They exhibit Fock space localization and long-range correlations robust against generic perturbations in a disorder-free scenario. In particular, we introduce a symmetry indicator method to enumerate cat scars, with which a set of unexpected inhomogeneous scar patterns are identified in addition to the ferromagnetic scars found before. These scars enforce DTC dynamics with rigid inhomogeneous patterns, offering a viable way to verify underlying eigenstate properties experimentally. Further, we prove rigorously that the strong Ising interactions enforce a selection rule for perturbations of different orders, which imposes an exponential suppression of spin fluctuations for Floquet eigenstates. Based on this property, three analytical scaling relations are proved to characterize the amplitudes, Fock space localization, and lifetime for DTC dynamics associated with cat scars. We further provide two practical methods to check whether certain DTC phenomena are dominated by single-spin dynamics or due to genuine interaction effects.
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