Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBeyond the universal Dyson singularity for 1-D chains with hopping disorder
129
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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.
rate research
Read More
We consider heat transport in one-dimensional harmonic chains attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation $d$ between any two successive impurities is randomly distributed according to a power-law distribution $P(d)sim 1/d^{alpha+1}$, being $alpha>0$. In the regime where the first moment of the distribution is well defined ($1<alpha<2$) the thermal conductivity $kappa$ scales with the system size $N$ as $kappasim N^{(alpha-3)/alpha}$ for fixed boundary conditions, whereas for free boundary conditions $kappasim N^{(alpha-1)/alpha}$ if $Ngg1$. When $alpha=2$, the inverse localization length $lambda$ scales with the frequency $omega$ as $lambdasim omega^2 ln omega$ in the low frequency regime, due to the logarithmic correction, the size scaling law of the thermal conductivity acquires a non-closed form. When $alpha>2$, the thermal conductivity scales as in the uncorrelated disorder case. The situation $alpha<1$ is only analyzed numerically, where $lambda(omega)sim omega^{2-alpha}$ which leads to the following asymptotic thermal conductivity: $kappa sim N^{-(alpha+1)/(2-alpha)}$ for fixed boundary conditions and $kappa sim N^{(1-alpha)/(2-alpha)}$ for free boundary conditions.
We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persists while for a larger number of chains a different qualitative behavior is generically expected, unless the many body interaction is vanishing. This is due to number theoretical properties of the frequency, similar to the ones assumed in KAM theory, and cancellations due to Pauli principle which in the single or two chains case imply that all the effective interactions are irrelevant; in contrast for a larger number of chains relevant effective interactions are present.
We investigate a tight-binding electronic chain featuring diagonal and off-diagonal disorder, these being modelled through the long-range-correlated fractional Brownian motion. Particularly, by employing exact diagonalization methods, we evaluate how the eigenstate spectrum of the system and its related single-particle dynamics respond to both competing sources of disorder. Moreover, we report the possibility of carrying out efficient end-to-end quantum-state transfer protocols even in the presence of such generalized disorder due to the appearance of extended states around the middle of the band in the limit of strong correlations.
We consider heat transport in one-dimensional harmonic chains with isotopic disorder, focussing our attention mainly on how disorder correlations affect heat conduction. Our approach reveals that long-range correlations can change the number of low-frequency extended states. As a result, with a proper choice of correlations one can control how the conductivity $kappa$ scales with the chain length $N$. We present a detailed analysis of the role of specific long-range correlations for which a size-independent conductivity is exactly recovered in the case of fixed boundary conditions. As for free boundary conditions, we show that disorder correlations can lead to a conductivity scaling as $kappa sim N^{varepsilon}$, with the scaling exponent $varepsilon$ being arbitrarily small (although not strictly zero), so that normal conduction is almost recovered even in this case.
We have studied the AC response of a hopping model in the variable range hopping regime by dynamical Monte Carlo simulations. We find that the conductivity as function of frequency follows a universal scaling law. We also compare the numerical results to various theoretical predictions. Finally, we study the form of the conducting network as function of frequency.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
