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

Abstract

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.

Anomalous transport through algebraically localized states in one dimension

“…The case of the critical AAH model (W = 2) in presence of long-range hopping, deserves to be studied even more thoroughly and there have been almost no work exploring this. Further, it has recently shown that isolated system transport properties and open system transport properties can be extremely different for quasi-periodic systems [8][9][10]. Thus, the open system transport properties of quasi-periodic one-dimensional systems with power-law hopping is also of extreme interest.…”

“…The physical effect of having such a mobility edge is that the same system can be conducting or insulating depending on energy. Quasi-periodic systems, with and without mobility edges are the limelight of recent research [8][9][10][11][12][13][14][15]. These systems have been experimentally realized in several set-ups, with tunable interactions [16][17][18][19][20][21][22].…”

Quasiperiodic quantum heat engines with a mobility edge

“…One important difference between the mobility edges appearing in the GAAH model and in the three-dimensional Anderson model is in the nature of the conducting states. The conducting states in the case of the GAAH model support ballistic transport [53], whereas those in the three-dimensional Anderson model support diffusive transport. As we will see, this has a major effect on the power output of our quasiperiodic quantum thermal machine.…”

“…The high temperature nonequilibrium phase diagram of the GAAH model has been explored in Ref. [53]. The precise knowledge of the position of the mobility edge for given values of λ and α makes the GAAH model ideal for investigation of low temperature thermoelectric properties in 1D quasiperiodic systems.…”

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

“…Another class of systems with the mobility edge by introducing a long-range hopping term [31] or a special form of the on-site incommensurate potential [52] present the energy-dependent self-duality in the compactly analytic form. Recently, great attention has been paid to the properties of the intermediate phase characterized by the mobility edge in the quasi-periodic lattices, such as many-body localization in the presence of a single particle mobility edge [53][54][55][56][57][58][59][60][61] and the existence of Bose glass phase in finite temperature [62,63]. Many works have been tried to understand the relations between the energy spectral property of a disordered system and the dynamical propagation of the wave packet .…”