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

  title={Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping},
  author={Akshay Krishna and R. N.Bhatt},
  journal={Physical Review B},
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 $\rho(E) \sim 1/|E \ln^3|E||$ and of the localization length $\xi(E) \sim |\ln|E||$, near the… 

Figures and Tables from this paper

Beyond the universal Dyson singularity for 1-D chains with hopping disorder
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
Dyson’s disordered linear chain from a random matrix theory viewpoint
  • P. Forrester
  • Physics, Mathematics
    Journal of Mathematical Physics
  • 2021
The first work of Dyson relating to random matrix theory, "The dynamics of a disordered linear chain”, is reviewed. Contained in this work is an exact solution of a so-called Type I chain in the case
Infinite randomness with continuously varying critical exponents in the random XYZ spin chain
We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrumbifurcation
Perturbative instability towards delocalization at phase transitions between MBL phases
We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet


Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
  • R. Metzler
  • Physics, Mathematics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2019
Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian
First passage and first hitting times of Lévy flights and Lévy walks
For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle
Effect of Hilbert space truncation on Anderson localization
The 1D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space,
Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
We investigate the magnetic susceptibility $\ensuremath{\chi}(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic couplings as a function of their spatial decay
Lévy flights versus Lévy walks in bounded domains.
This work investigates analytically and numerically whether and under which conditions both approaches yield similar results in terms of selected statistical observables characterizing the motion: the survival probability, mean first passage time, and stationary probability density functions.
Super Generalized Central Limit Theorem —Limit Distributions for Sums of Non-identical Random Variables with Power Laws—
The power law is present ubiquitously in nature and in our societies. Therefore, it is important to investigate the characteristics of power laws in the current era of big data. In this paper we
Classification of topological quantum matter with symmetries
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum
Generalized Dyson model: Nature of the zero mode and its implication in dynamics
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
From disordered quantum walk to physics of off-diagonal disorder
Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible
Lévy walks
  • Rev. Mod. Phys
  • 2015