Localization-delocalization transition in the random dimer model

Abstract

The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions, and without modifying the impurity correlations.PACS numbers: 64.60. Cn,67.60.Bc In a one-dimensional disordered system, Anderson localization is known to occur at any energy when the disorder is δ correlated [1,2]. Nevertheless, if one introduces particular short-range correlations, delocalization of a significant subset of the eigenstates can appear. This happens in the random-dimer model (RDM) [3], in which the sites of a lattice are assigned energies ǫ a or ǫ b at random, with the additional constraint that sites of energy ǫ b always appear in pairs, or dimers. The same occurs in its dual counterpart (DRDM) [3], in which lattice sites with energy ǫ b never appear as neighbors. In these models, extended states arise from resonant modes of the (dual)dimers which present vanishing backscattering at energy E res . In the thermodynamic limit, the ratio √ N /N between the number of delocalized states and the total number of states vanishes, and there is no mobility edge separating extended and localized energy eigenstates. Nevertheless in finite size systems, thus in real systems, a localization-delocalization transition can be induced by driving E res inside the spectrum.This model was proposed to be the possible mechanism which leads to the insulator-metal transition in a wide class of conducting polymers such as polyaniline and heavily doped polyacetylene (see, for instance, [4]) and in some biopolymers such as DNA [5,6]. The evidence of delocalized electronic states was experimentally demonstrated in a random-dimer GaAs-AlGaAs superlattice [7], while for photons, a RDM dielectric system was used [8]. Recently, a RDM setup has been proposed to demonstrate the delocalization of acoustic waves [9]. For polymers, semiconductor lattices, photonic crystals and elastic chains, the dimer resonant energies cannot be modified without changing the sample itself. Thus the localization-delocalization transition for a (D)RDM chain as a function of the relative position of the resonant modes with respect to the band modes cannot easily be studied using these physical systems.In this article, we propose an experimental procedure to realize a DRDM experiment with a one-dimensional (1D) two-component ultracold atomic mixture in an optical lattice, and we demonstrate that the localizationdelocalization transition can be explored by tuning the interparticle interactions.To introduce disorder, a component (B d ) has ...

Localization of an inhomogeneous Bose-Einstein condensate in a moving random potential

“…All these factors are not taken into account in the current optical model. Finally, let us remark that both the single bump and the single dimer yield full delocalization (R = 0) for α = π, namely when each bump plays the role of a cavity [4,26], corresponding to v ≫ c in our system.…”

“…Such a disorder potential could be realized by deeply trapping some impurities (heavy atoms of another species) in an optical lattice strongly detuned from the condensate atomic frequencies [24][25][26]. When the disorder pattern is pulled with a constant speed v through the system, if v is lower than the sound speed c = µ/(2m) [27], we expect the disorder not to affect the system because of the superfluid nature of the gas itself [20].…”

Role of Correlations and Off-Diagonal Terms in Binary Disordered One-Dimensional Systems

“…In the binary disordered systems correlations can take a form of N -mers where frozen particles always come in series of length N , or dual random dimer model (DRDM) where no two frozen particles can appear on the adjacent sites. Such correlations can be created by using several lattices with different lattice constants (as described for the case of the DRDM in [24]). …”

Universal scheme to generate metal–insulator transition in disordered systems

“…However, Anderson localization breaks down in the random binary alloy when correlations are introduced in the disorder distribution. A discrete number of extended states have been reported in the random-dimer model [18][19][20] and its generalized versions [21,22], where one or both sites always appear in n-mer. A band of extended states will emerge in the binary alloy when the site energies are long-range correlated [23].…”

“…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.…”