Publisher’s Note: Localization in one-dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models [Phys. Rev. B<b>83</b>, 075105 (2011)]

Biddle, John; Priour, Donald; Wang, B.; Sarma, S. Das

doi:10.1103/physrevb.83.089901

Cited by 39 publications

(59 citation statements)

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“…Furthermore, if there is a single localization transition between these two phases it must be at exactly v c = 1, where the model is invariant under the duality. This is indeed the case for the AA model (although there are variations that experience a richer transition [12][13][14][15][16][17][18][19][20][21][22] , so self-duality alone does not imply a single transition that occurs simultaneously at all energies). Now let's consider adding a weak site-random potential to this model.…”

Section: 6mentioning

confidence: 92%

Anderson localization transitions with and without random potentials

Devakul

Huse

2017

Phys. Rev. B

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We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-André model to higher dimensions. In three dimensions (3D) we find that the Anderson localization transitions appear to be in the same universality class as for random potentials. In scaling or renormalization group terms, this means that randomness of the potential is irrelevant at the Anderson localization transitions in 3D. In two dimensions (2D) we also explore the Ando model, which is in the symplectic symmetry class and shows an Anderson localization transition for random potentials. Here, unlike in 3D, we find that the universality class changes when we instead use a quasiperiodic potential.

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Section: 6mentioning

confidence: 92%

Anderson localization transitions with and without random potentials

Devakul

Huse

2017

Phys. Rev. B

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“…Even though the AAH model has no mobility edge, various generalizations of it, as well as other quasiperiodic systems, have been shown to have mobility edges in one dimension. Recently, physics of such systems have attracted a lot of attention [23][24][25][26][27][28][29][30][31][32][33][34][35] and has also been experimentally realized [36]. In this paper, we focus on one such model that has been recently proposed [23][24][25][26][27].…”

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confidence: 99%

Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

2017

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We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-André-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current, calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a 'critical' line separating regions of ballistic and localized transport. Like the critical point of AAH model, current scales sub-diffusively with system size on the 'critical' line (I ∼ N −2±0.1 ). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where I ∼ N −1.4±0.05 ). All these results can be understood from the above-mentioned connection between states near mobility edge of GAAH model and those of critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.Introduction: Anderson localization is a phenomenon seen in a wide class of systems [1][2][3]. It refers to spatial localization of energy eigenstates in the presence of uncorrelated disorder and in absence of interactions. In one and two dimensions, even a small amount of disorder makes all energy eigenstates localized. In three dimensions, beyond a critical strength of disorder, there occurs a mobility edge [4] separating localized and extended eigenstates. Understanding the physics of such a three dimensional system from a microscopic model is difficult. As a result, it is of interest to develop and study, theoretically and experimentally, lower dimensional models with a mobility edge.

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“…A band of extended states will emerge in the binary alloy when the site energies are long-range correlated [23]. In addition, other theoretical models have been suggested to produce conducting states in low-dimensional disordered systems [24][25][26][27][28][29][30][31][32][33], and some of them have been corroborated in GaAs-AlGaAs superlattices [34] and Bose-Einstein condensate (BEC) [14]. Nevertheless, we notice that all electronic states become localized in these correlated disordered systems when the disorder degree is extremely large.…”

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confidence: 68%

“…3(b) we obtain β=−1], due to the Anderson localization effects, although they possess either the diagonal disorder (dashed lines) or the off-diagonal disorder (dotted lines) and are more ordered than the former case. the disorder degree is very large [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], we can see from Fig. 3(c) that ξ L is independent of W for the former ladder and all states are always extended in the gray energy region [ Fig.…”

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confidence: 99%

Universal scheme to generate metal–insulator transition in disordered systems

Guo

Xiong

Xie

et al. 2013

J. Phys.: Condens. Matter

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We propose a scheme to generate metal-insulator transition in random binary layer (RBL) model, which is constructed by randomly assigning two types of layers. Based on a tight-binding Hamiltonian, the localization length is calculated for a variety of RBLs with different cross section geometries by using the transfer-matrix method. Both analytical and numerical results show that a band of extended states could appear in the RBLs and the systems behave as metals by properly tuning the model parameters, due to the existence of a completely ordered subband, leading to a metal-insulator transition in parameter space. Furthermore, the extended states are irrespective of the diagonal and off-diagonal disorder strengths. Our results can be generalized to two-and three-dimensional disordered systems with arbitrary layer structures, and may be realized in Bose-Einstein condensates.

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Publisher’s Note: Localization in one-dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models [Phys. Rev. B83, 075105 (2011)]

Cited by 39 publications

References 0 publications

Anderson localization transitions with and without random potentials

Anderson localization transitions with and without random potentials

Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

Universal scheme to generate metal–insulator transition in disordered systems

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