scholarly journals Mobility Edges in One-dimensional Disordered Aharonov-Bohm Rings

2019 ◽  
Vol 29 (4) ◽  
pp. 471
Author(s):  
Phi Ba Nguyen
Keyword(s):  
Tight Binding ◽  
System Size ◽  
Disorder Strength ◽  
Weak Disorder ◽  
Localization Transition ◽  
One Dimensional ◽  
Energy Disorder ◽  
Hamiltonian Model ◽  
Aharonov Bohm ◽  
Flux Energy

We study numerically the localization properties of the eigenstates of a tight-binding Hamiltonian model for noninteracting electrons moving in a one-dimensional disordered ring pierced by an Aharonov-Bohm flux. By analyzing the dependence of the inverse participation ratio on Aharonov-Bohm flux, energy, disorder strength and system size, we find that all states in the ring are delocalized in the weak disorder limit. The states lying deeply in the band tails will undergo a continuous delocalization-localization transition as the disorder strength in the ring sweeps from the weak to the strong disorder regime.

scholarly journals Signatures of a critical point in the many-body localization transition

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Ángel L. Corps ◽  
Rafael Molina ◽  
Armando Relaño
Keyword(s):  
Singular Point ◽  
Critical Point ◽  
Chaotic Behavior ◽  
Finite Size ◽  
System Size ◽  
Disorder Strength ◽  
Many Body ◽  
Localization Transition ◽  
Spectral Statistics ◽  
The Many

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

scholarly journals Probing the Global Delocalization Transition in the de Moura-Lyra Model with the Kernel Polynomial Method

2020 ◽  
Vol 233 ◽  
pp. 05011
Author(s):  
N.A. Khan ◽  
J.P. Santos Pires ◽  
J.M. Viana Parente Lopes ◽  
J.M.B. Lopes dos Santos
Keyword(s):  
Nearest Neighbor ◽  
Tight Binding ◽  
Localization Length ◽  
Polynomial Method ◽  
Tight Binding Model ◽  
Weak Disorder ◽  
Binding Model ◽  
One Dimensional ◽  
Open Boundaries ◽  
Kernel Polynomial Method

In this paper, we report numerical calculations of the localization length in a non-interacting one-dimensional tight-binding model at zero tem¬perature, holding a correlated disorder model with an algebraic power-spectrum (de Moura-Lyra model). Our calculations were based on a Kernel Polynomial implementation of the Thouless formula for the inverse localization length of a general nearest-neighbor 1D tight-binding model with open boundaries. Our results confirm the delocalization of all eigenstates in de Moura-Lyra model for α > 1 and a localization length which diverges as ξ ∝ (1 – α)–1 for α → 1–, at all energies in the weak disorder limit (as previously seen in [12]).

STRANGE EFFECT OF DISORDER ON ELECTRON TRANSPORT THROUGH A THIN FILM

2008 ◽  
Vol 07 (02n03) ◽  
pp. 171-178
Author(s):  
SANTANU K. MAITI
Keyword(s):  
Thin Film ◽  
Electron Transport ◽  
Disordered Systems ◽  
Tight Binding ◽  
Finite Size ◽  
Anomalous Behavior ◽  
Disorder Strength ◽  
Weak Disorder ◽  
Binding Model ◽  
Strong Disorder

A novel feature of electron transport is explored through a thin film of varying impurity density with the distance from its surface. The film, attached to two metallic electrodes, is described by simple tight-binding model and its coupling to the electrodes is treated through Newns–Anderson chemisorption theory. It is observed that in the strong disorder regime the amplitude of the current passing through the film increases with the increase of the disorder strength, while it decreases in the weak disorder regime. This anomalous behavior is completely opposite to that of conventional disordered systems. Our results also predict that the electron transport is significantly influenced by the finite size of the thin film.

scholarly journals Optoelectronic properties of one-dimensional molecular chains simulated by a tight-binding model

AIP Advances ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 015127
Author(s):  
Qiuyuan Chen ◽  
Jiawei Chang ◽  
Lin Ma ◽  
Chenghan Li ◽  
Liangfei Duan ◽  
...  
Keyword(s):  
Tight Binding ◽  
Optoelectronic Properties ◽  
Tight Binding Model ◽  
Binding Model ◽  
One Dimensional

scholarly journals LOCALIZED ENTANGLEMENT IN ONE-DIMENSIONAL ANDERSON MODEL

2005 ◽  
Vol 19 (11) ◽  
pp. 517-527 ◽  
Author(s):  
HAIBIN LI ◽  
XIAOGUANG WANG
Keyword(s):  
Anderson Model ◽  
Localization Length ◽  
Direct Relation ◽  
Disorder Strength ◽  
One Dimensional ◽  
Entanglement Distribution ◽  
Localization Center

The entanglement in one-dimensional Anderson model is studied. The pairwise entanglement has a direct relation to the localization length and is reduced by disorder. Entanglement distribution displays the entanglement localization. The pairwise entanglements around localization center exhibit a maximum as the disorder strength increases. The dynamics of entanglement are also investigated.

Symmetry Violations in Partially Oxidized One-Dimensional (1D)Transition Metal Polymers. Metal-Ligand-Metal(M-L-M) Bridged Systems

1984 ◽  
Vol 39 (9) ◽  
pp. 807-829
Author(s):  
Michael C. Böhm
Keyword(s):  
Transition Metal ◽  
Density Wave ◽  
Tight Binding ◽  
Mean Field ◽  
Valence Bond ◽  
Hole State ◽  
One Dimensional ◽  
Metal Derivatives ◽  
A Charge ◽  
Metal Ligand

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d-2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN)2-5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

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