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

Akshay Krishna, R. N. Bhatt

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number168537
JournalAnnals of Physics
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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