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Information Recording Materials

Electronic States in One-Dimensional Correlated Disorder Systems

AN Jun-cheng

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The effects of long-range power-law correlation on the intrinsic energy,intrinsic wave function and entanglement of one-dimensional disorder system were studied,and the changes of localization were observed.The results show that the entanglement of the three measures is fully enough to reflect the properties of correlation.As an example of correlation,the entanglement of DNA molecular chain was studied using the Anderson model.The results show that the entanglement has similar properties with the correlation and reflects the properties of the correlation.

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The effects of long-range power-law correlation on the intrinsic energy,intrinsic wave function and entanglement of one-dimensional disorder system were studied,and the changes of localization were observed.The results show that the entanglement of the three measures is fully enough to reflect the properties of correlation.As an example of correlation,the entanglement of DNA molecular chain was studied using the Anderson model.The results show that the entanglement has similar properties with the correlation and reflects the properties of the correlation.
By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin–Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain: guanine (G), adenine (A), cytosine(C), thymine (T). This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.
The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the entanglement.
During this Ph.D, we studied one-dimensional systems with long-range couplings. In the first part, we demonstrate that power-law couplings lead to an algebraic decay of correlations at long distances in disordered quantum wires. In the second chapter, we analyzed an extended Hubbard model where particles interact via a finite-range potential that induces frustration and new exotic phases. In the third chapter, we demonstrated that restoring energy extensivity has an influence on the low-energy properties of quantum model in the thermodynamic limit. Finally, we provide preliminary results on the modification of Anderson localization due to the coupling to a cavity mode.
We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ensuremath{\ell}$ as a power law $1/{\ensuremath{\ell}}^{\ensuremath{\alpha}}$. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long-distance algebraic decay of correlations within disordered-localized phases, for all exponents $\ensuremath{\alpha}$. The exponent of algebraic decay depends only on $\ensuremath{\alpha}$, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular, and solid-state physics.
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as [Formula: see text], where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.
We investigate the Mott-Anderson physics in interacting disordered one-dimensional chains through the average single-site entanglement quantified by the linear entropy, which is obtained via density-functional theory calculations. We show that the minimum disorder strength required to the so-called full Anderson localization-characterized by the real-space localization of pairs-is strongly dependent on the interaction regime. The degree of localization is found to be intrinsically related to the interplay between the correlations and the disorder potential. In magnetized systems, the minimum entanglement characteristic of the full Anderson localization is split into two, one for each of the spin species. We show that although all types of localization eventually disappear with increasing temperature, the full Anderson localization persists for higher temperatures than the Mott-like localization.