Finite size effects in infinitely large electronic systems with correlated disorders

Nishino, Seiji; Yakubo, Kousuke; Shima, Hiroyuki

doi:10.1103/physrevb.79.033105

Cited by 12 publications

(12 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1(c) and (d), even in the thermodynamic limit. 32 Due do this peculiar behavior, we consider the IPR ν only for single disorder realizations. Interestingly, for the current model, 32 the positions of the mobility edges in a given sample are determined by sharp peaks in the IPR ν , which separate the extended states (N × IPR ν constant) from the localized ones (N × IPR ν size dependent), Figs.…”

Section: A Density Of States and Inverse Participation Ratiomentioning

confidence: 99%

Anderson localization and momentum-space entanglement

2014

View full text Add to dashboard Cite

We consider Anderson localization and the associated metal-insulator transition for noninteracting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the wavefunction, we follow a recent proposal to study momentum-space entanglement. For a D = 1 model with long-range disorder correlations, both the entanglement spectrum and the entanglement entropy allow us to clearly distinguish between extended and localized states based upon a single realization of disorder. However, for other models including the D = 2 case with long-range correlated disorder, we find that the method is not similarly successful. We analyze the reasons for its failure, concluding that the much desired generalization to higher dimensions may be problematic.

show abstract

Section: A Density Of States and Inverse Participation Ratiomentioning

confidence: 99%

Anderson localization and momentum-space entanglement

2014

View full text Add to dashboard Cite

show abstract

“…Similarly to the case of short-range correlation, we first consider the case of a longrange correlated real random potential. Although this case was already considered extensively [12,13,[15][16][17][18][19][20], we present it here in a slightly different manner. In Figure 6, we show the participation number P as a function of the system size N for different values of the correlation strength α (= 0, 0.25, the disorder strength W is fixed to 2.…”

Section: Long-range Correlationsmentioning

confidence: 99%

“…During the recent few decades, the influence of spatial disorder correlations on the localization properties has been studied extensively [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. It has been demonstrated both theoretically and experimentally that some special types of short-range correlated disorder can produce extended eigenstates even in one dimension [10,11,26].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations

Nguyen,

Lieu,

Kim

2019

Preprint

View full text Add to dashboard Cite

We study numerically the effects of short-and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part of the on-site potential is random. We calculate participation number versus strengths of disorder and correlation. In the short-ranged case and when the correlation length is sufficiently small, we find that there exists a critical value of the disorder strength, below which enhancement and above which suppression of localization occurs as the correlation length increases. In the region where the correlation length is larger, localization is suppressed in all cases. A similar behavior is obtained for long-range correlations as the disorder strength and the correlation exponent are varied. Unlike in the case of a long-range correlated real random potential, no signature of the localization transition is found in a long-range correlated imaginary random potential. In the region where localization is enhanced in the presence of long-range correlations, we find that the enhancement occurs in the whole energy band, but is strongest near the band center. In addition, we find that the anomalous localization enhancement effect occurs near the band center in the long-range correlated case.

show abstract

“…The error bars represent the standard deviation of the population (instead of the estimated standard deviation of the average) since, as pointed out in Ref. 41, in the presence of long-range correlations sample-to-sample fluctuations survive in the thermodynamic limit.…”

Section: D Anderson Model With Correlated Disordermentioning

confidence: 99%

Kohn's localization in disordered fermionic systems with and without interactions

Varma

Pilati

2015

Phys. Rev. B

View full text Add to dashboard Cite

Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-André Hamiltonian and its modification including next-nearest neighbour hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localisation tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then we investigate the effect of weak repulsive interactions in the Aubry-André Hamiltonian, a model which describes a recent coldatoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalisation induced by interactions.

show abstract

Finite size effects in infinitely large electronic systems with correlated disorders

Cited by 12 publications

References 25 publications

Anderson localization and momentum-space entanglement

Anderson localization and momentum-space entanglement

Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations

Kohn's localization in disordered fermionic systems with and without interactions

Contact Info

Product

Resources

About