Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping Article Swipe

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Akshay Krishna , R. N. Bhatt · YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1103/physrevb.101.224203

Here, 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 sublattice symmetry, for each realization). For nonsingular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) ~ 1/|E\\: \\text{ln}^3 |E||$ and of the localization length $ξ(E) ~ |\\text{ln}|E||$, near the band center $\\textit{E}$ = 0 . (This singular behavior is also applicable to random $\\textit{XY}$ and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain.) Simultaneously, the state at$\\textit{E}$ = 0 shows a universal, subexponential decay at large distances $\\sim \\text{exp}[–\\sqrt{r/r_0}]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $\\textit{t}$ is of the form $\\sim 1/[t \\text{ln}^{λ+1}(1/t)]$, 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 nonuniversal 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 $\\textit{E}$ = 0 state at large distances also deviates from the universal result and is of the form $\\sim\\text{exp}[–(r/r_0)^{1/λ}]$ , which decays faster than an exponential for λ < 1.

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https://doi.org/10.1103/physrevb.101.224203

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https://doi.org/10.1103/physrevb.101.224203

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Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping

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article

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en

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2020

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2020-06-15

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Akshay Krishna, R. N. Bhatt

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https://doi.org/10.1103/physrevb.101.224203

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Lambda, Physics, Singularity, Lattice (music), k-nearest neighbors algorithm, Quantum mechanics, Realization (probability), Mathematical physics, Mathematics, Mathematical analysis, Statistics, Acoustics, Artificial intelligence, Computer science

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