多体临界相的渐近可解模型：迁移率边、疤痕与倒置疤痕
An asymptotically solvable model of many-body critical phases: mobility edges, scars, and inverted scars
AI总结：
本研究构建一维近邻相互作用自旋链的渐近可解模型，发现其存在由多体迁移率边分隔的两个相，含多体疤痕与倒置疤痕，挑战准周期MBL无雪崩不稳定性的普遍认知。
AI中文摘要：
随机多体局域化（MBL）系统的预热 regime 由偶然多体共振主导，而大型确定性系统中预期存在另一类源于底层势结构的共振。已知这类共振可产生既非局域也非扩展的单粒子临界相，但其在相互作用系统中的后果仍不清楚。本工作构建了一维近邻相互作用自旋链的渐近可解模型，其空间结构诱导出层级化的类镜面多体共振。我们在热力学极限下推导出两个相，分别满足和违反弱本征态热化假设（ETH）的某一版本。这两个相与常规MBL相和ETH相类似，但存在稀有本征态表现为相反相，被解释为多体疤痕和倒置疤痕。令人惊讶的是，这两个相可被有限温度相变分隔，对应热力学多体迁移率边，而此前普遍认为这不可能存在。我们的结果还表明，在原本局域的相互作用 Aubry-André 模型中存在离域稀有区域，即使不存在随机系统中那样的低无序区域，这挑战了准周期MBL不存在雪崩不稳定性的普遍认知。
英文摘要：
While the prethermal regime of random many-body localized (MBL) systems is dominated by accidental many-body resonances, another class of resonances, originating from the underlying potential structure, is expected in large-size deterministic systems. It is known that this class of resonances can lead to single-particle critical phases that are neither localized nor extended, but the consequences in interacting systems remain unclear. In this work, we construct an asymptotically solvable model of a one-dimensional nearest-neighbor interacting spin chain, whose spatial structure induces a hierarchy of mirror-like many-body resonances. We derive two phases in the thermodynamic limit, characterized by the satisfaction and violation of a version of the weak eigenstate thermalization hypothesis (ETH). While these two phases are similar to the usual MBL and ETH phases, there exist rare eigenstates that behave like the opposite phase, interpreted as many-body scars and inverted scars. Surprisingly, the two phases can be separated by a finite-temperature phase transition, corresponding to a thermodynamic many-body mobility edge, which was often believed to be impossible. Our results also suggest the existence of delocalized rare regions in an otherwise-localized interacting Aubry-André model, even if there are no low-disorder regions like those in random systems. This challenges the common belief that there is no avalanche instability in quasiperiodic MBL.
