Beyond the universal Dyson singularity for 1-D chains with hopping disorder

• URL: http://arxiv.org/abs/2107.08518v1
• Date: Sun, 18 Jul 2021 19:07:19 GMT
• Title: Beyond the universal Dyson singularity for 1-D chains with hopping disorder
• Authors: Akshay Krishna and R. N. Bhatt
• Abstract summary: We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain - that of random walks and diffusion with anomalous exponents.

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