广义Dyson模型：零模的性质及其动力学意义
Generalized Dyson model: nature of zero mode and its implication in dynamics
摘要：
研究了一维具有手征对称性和关联键无序的非相互作用费米子链中反常$E=0$态在动力学性质中的作用。这些模型解释了零能量下的发散态密度，导致带中心的发散局域化长度。通过分析计算的本地化长度为有限的系统，我们表明，在无序的相关性修改的空间衰减的$E = 0$状态从准本地化扩展。我们数值模拟电荷和纠缠传播，并提供证据表明，接近$E=0$的状态占主导地位的动力学性质。值得注意的是，我们发现，相关导致subdiffusive电荷传播，而纠缠的增长是grammically缓慢。还观察到纠缠饱和度与系统尺寸的对数标度，这表明类似于量子临界玻璃的行为。
英文摘要：
We study the role of the anomalous $E=0$ state in dynamical properties of non-interacting fermionic chains with chiral symmetry and correlated bond disorder in one dimension. These models posses a diverging density of states at zero energy leading to a divergent localization length at the band center. By analytically calculating the localization length for a finite system, we show that correlations in the disorder modify the spatial decay of the $E = 0$ state from being quasilocalized to extended. We numerically simulate charge and entanglement propagation and provide evidence that states close to $E=0$ dominate the dynamical properties. Remarkably, we find that correlations lead to subdiffusive charge propagation, whereas the growth of entanglement is logarithmically slow. A logarithmic scaling of entanglement saturation with system size is also observed, which indicates a behavior akin to quantum critical glasses.
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