Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban

Band Structure for the Concurrence in 1D Long-range Correlated Disorder System

Zhang Yuan-sheng

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The concurrence of the ground state in 1D,Anderson diagonalized-disorder model is studied and the existence of the band structure of the concurrence in the longer sequence case is demonstrated in terms of the long-range correlations.Moreover,the band structure of the concurrence and its width with the sequence is discussed in the paper.The result shows that the width of the band structure becomes narrow with the increase of the sequence.

Related papers

ENTANGLEMENT IN ONE-AND TWO-DIMENSIONAL ANDERSON MODELS WITH LONG-RANGE CORRELATED-DISORDER

Z. Z. Guo, Z. G. XUAN, Y. S. ZHANG +1 more

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.

International Journal of Quantum Information•Aug 1, 2009•0 citations

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

Guo Zi-zheng

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.

Chinese Physics Letters•Mar 1, 2008•4 citations

Semi-localized ground state in a 1D system with long-range hopping

M. S. Bahovadinov, Faridun N. Jalolov, V. E. Kravtsov +2 more

We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1

arXiv:2608.25806•Aug 26, 2026•0 citations

Ground-state phases of interacting Fermi gases in disordered one-dimensional lattices

Gao Xianlong

We numerically investigate a one-dimensional Anderson–Hubbard model under harmonic confinement. The effects of disorder on the ground-state properties are studied for Gaussian-correlated disorder and random impurities upon changing the amplitude of the disorder strength, the correlation length or the number of impurities. For a large disorder correlation length, both the band- and Mott-insulating phases re-enter naturally as a result of a smooth long-range correlated disorder. For the randomly distributed impurities in a system of composite Mott- and band-insulating phases, we find that the band-insulating region is rapidly destroyed while the Mott region is more robust against the increase of impurities. The fluid regions are less affected in this case.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 2, 2012•4 citations

Ground-state spin structure of strongly interacting disordered 1D Hubbard model

Eli Eisenberg, Richard Berkovits

Abstract. We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite-U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron–electron repulsion, U, which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka [1] states that in theU D 1 limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown [2] that for open boundary conditions (BCs) the GS for finiteU is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U, the GS of

•Jan 1, 1999•4 citations

Critical behavior of the two-dimensional Anderson model with long-range correlated disorder

Israel Faustino dos Santos, F. A. B. F. de Moura, M. L. Lyra +1 more

We describe the critical behavior of the Anderson-like transition predicted to occur in the 2D tight-binding model with isotropic scale-free long-range correlated disorder characterized by a power-law spectral density. We explore the scale invariance of the participation function relative fluctuation at the critical point to locate the mobility edge as a function of the power-law spectral density exponent α 2D . The states near the band center, which exhibit power-law localization for uncorrelated disorder, become delocalized for α 2D >2. In addition, we consider the finite-size scaling hypothesis to estimate the correlation length critical exponent. We find that the critical exponent ν depends on α 2D , thus indicating that correlations in the disorder distribution are indeed relevant in this regime, in agreement with the extended Harris criterion.

Journal of Physics Condensed Matter•Nov 1, 2007•33 citations
The concurrence of the ground state in 1D,Anderson diagonalized-disorder model is studied and the existence of the band structure of the concurrence in the longer sequence case is demonstrated in terms of the long-range correlations.Moreover,the band structure of the concurrence and its width with the sequence is discussed in the paper.The result shows that the width of the band structure becomes narrow with the increase of the sequence.
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.
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.
We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes t(r)∝r−at(r)\propto r^{-a}t(r)∝r−a. In contrast to the standard one-dimensional Anderson model (a→∞a\to\inftya→∞), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1
We numerically investigate a one-dimensional Anderson–Hubbard model under harmonic confinement. The effects of disorder on the ground-state properties are studied for Gaussian-correlated disorder and random impurities upon changing the amplitude of the disorder strength, the correlation length or the number of impurities. For a large disorder correlation length, both the band- and Mott-insulating phases re-enter naturally as a result of a smooth long-range correlated disorder. For the randomly distributed impurities in a system of composite Mott- and band-insulating phases, we find that the band-insulating region is rapidly destroyed while the Mott region is more robust against the increase of impurities. The fluid regions are less affected in this case.
Abstract. We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite-U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron–electron repulsion, U, which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka [1] states that in theU D 1 limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown [2] that for open boundary conditions (BCs) the GS for finiteU is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U, the GS of
We describe the critical behavior of the Anderson-like transition predicted to occur in the 2D tight-binding model with isotropic scale-free long-range correlated disorder characterized by a power-law spectral density. We explore the scale invariance of the participation function relative fluctuation at the critical point to locate the mobility edge as a function of the power-law spectral density exponent α 2D . The states near the band center, which exhibit power-law localization for uncorrelated disorder, become delocalized for α 2D >2. In addition, we consider the finite-size scaling hypothesis to estimate the correlation length critical exponent. We find that the critical exponent ν depends on α 2D , thus indicating that correlations in the disorder distribution are indeed relevant in this regime, in agreement with the extended Harris criterion.