论文标题
超越一维链中的普遍行为，随机最近的邻居跳跃
Beyond universal behavior in the one-dimensional chain with random nearest neighbor hopping
论文作者
论文摘要
我们研究具有独立分布的随机跳跃且无现场电位的电子的一维邻居紧密结合模型（即带有颗粒 - 孔对称性的异性疾病，导致每个实现，导致亚晶状体对称性）。对于跳跃的非单明性分布，众所周知，该模型表现出状态密度的通用，奇异的行为$ρ（e）\ sim 1/| e \ ln^3 | e || $以及本地化的长度$之一\ sim | | | \ sim | \ sim | \ sim | \ ln | e | e | e || （这种奇异行为也适用于随机XY和海森堡自旋链；戴森最初是为特定的随机谐波振荡器链获得的）。同时，$ e = 0 $的状态在较大距离处显示了通用的，子指数的衰减$ \ sim \ exp [ - \ sqrt {r/r_0}] $。在这项研究中，我们考虑了跳跃的单数但可正常化的分布，其小$ t $的行为是$ \ sim 1/ [t \ ln^{λ+1}（1/ t）$的形式，其特征是单个，连续可调的参数$λ> 0 $。我们发现，使用分析方法和数值方法的组合，尽管通用结果适用于$λ> 2 $，但它不再在$ 0 <λ<2 $的间隔中保留。特别是，我们发现状态密度奇异性的形式以连续的方式增强（相对于dyson结果），具体取决于非大学参数$λ$；同时，定位长度在低能量下显示出较小的形式，并停止以下差异以下$λ= 1 $。对于$λ<2 $，$ e = 0 $状态在大距离处的损坏也与通用结果偏离，并且是$ \ sim \ exp的形式的差异[ - （r/r_0）^{1/λ}] $，该^{1/λ}] $比$λ<1 $的指数更快。
We study the one-dimensional nearest neighbor tight binding model of electrons with independently distributed random hopping and no on-site potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to sub-lattice symmetry, for each realization). For non-singular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) \sim 1/|E \ln^3|E||$ and of the localization length $ξ(E) \sim |\ln|E||$, near the band center $E = 0$. (This singular behavior is also applicable to random XY and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain). Simultaneously, the state at $E = 0$ shows a universal, sub-exponential decay at large distances $\sim \exp [ -\sqrt{r/r_0} ]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $t$ is of the form $\sim 1/ [t \ln^{λ+1}(1/t) ]$, characterized by a single, continuously tunable parameter $λ> 0$. We find, using a combination of analytic and numerical methods, that while the universal result applies for $λ> 2$, it no longer holds in the interval $0 < λ< 2$. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the non-universal parameter $λ$; simultaneously, the localization length shows a less divergent form at low energies, and ceases to diverge below $λ= 1$. For $λ< 2$, the fall-off of the $E = 0$ state at large distances also deviates from the universal result, and is of the form $\sim \exp [-(r/r_0)^{1/λ}]$, which decays faster than an exponential for $λ< 1$.
