Anomalous transport in the Aubry-André-Harper model in isolated and open systems

Purkayastha, Archak; Sanyal, Subrata; Dhar, Abhishek; Kulkarni, Manas

doi:10.1103/physrevb.97.174206

Cited by 73 publications

(86 citation statements)

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“…The effect of other irrational numbers is also an interesting question. Also, it has been recently shown that the critical AAH model has remarkably different transport behaviors in closed and open system set-ups [13]. Detailed investigation of closed system transport, as well as, low temperature transport of GAAH model is thus of great interest and will be taken up in a future work.…”

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confidence: 98%

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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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confidence: 98%

“…The eigenstates at the critical point are neither totally delocalized nor localized, but are 'critical' [12]. The transport properties at the critical point of AAH model has been studied recently in [13], and subsequently in FIG. 1.…”

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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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“…The particle and heat currents in a one-dimensional system among two fermionic reservoirs, within the WBL approximation and in the weak system-bath coupling limit, can be expressed directly as a function of the eigenstates of the isolated system [52]:…”

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confidence: 99%

Quasiperiodic quantum heat engines with a mobility edge

Cecilia

Mitchison

Purkayastha

et al. 2020

Phys. Rev. Research

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Steady-state thermoelectric machines convert heat into work by driving a thermally generated charge current against a voltage gradient. In this work, we propose a new class of steady-state heat engines operating in the quantum regime, where a quasiperiodic tight-binding model that features a mobility edge forms the working medium. In particular, we focus on a generalization of the paradigmatic Aubry-André-Harper (AAH) model, known to display a single-particle mobility edge that separates the energy spectrum into regions of completely delocalized and localized eigenstates. Remarkably, these two regions can be exploited in the context of steadystate heat engines as they correspond to ballistic and insulating transport regimes. This model also presents the advantage that the position of the mobility edge can be controlled via a single parameter in the Hamiltonian. We exploit this highly tunable energy filter, along with the peculiar spectral structure of quasiperiodic systems, to demonstrate large thermoelectric effects, exceeding existing predictions by several orders of magnitude. This opens the route to a new class of highly efficient and versatile quasiperiodic steady-state heat engines, with a possible implementation using ultracold neutral atoms in bichromatic optical lattices. arXiv:1908.05139v2 [cond-mat.dis-nn]

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“…It is well-known that the mean of such a probability distribution is undefined for p < 2. To check this explicitly, we note that f N x0 dx xP n (x) ∼ N 2−p , ∀ p = 2 log(N ), ∀ p = 2 (9) Thus, the RHS diverges with system-size for p ≤ 2. So, according to our localization-delocalization criterion Eq.…”

Section: B Localization and Transportmentioning

confidence: 99%

“…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].…”

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Anomalous transport through algebraically localized states in one dimension

2019

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Localization in one-dimensional disordered or quasiperiodic non-interacting systems in presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed to exponential localization in short-ranged systems. Exponential localization is synonymous with insulating behavior in the thermodynamic limit. Here we show that the same is not true for algebraic localization. We show, on general grounds, that depending on the strength of the algebraic decay, the algebraically localized states can be actually either conducting or insulating in thermodynamic limit. We exemplify this statement with explicit calculations on the Aubry-André-Harper model in presence of power-law hopping, with the powerlaw exponent α > 1, so that the thermodynamic limit is well-defined. We find a phase of this system where there is a mobility edge separating completely delocalized and algebraically localized states, with the algebraically localized states showing signatures of super-diffusive transport. Thus, in this phase, the mobility edge separates two kinds of conducting states, ballistic and super-diffusive. We trace the occurrence of this behavior to near-resonance conditions of the on-site energies that occur due to the quasi-periodic nature of the potential.

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Anomalous transport in the Aubry-André-Harper model in isolated and open systems

Cited by 73 publications

References 75 publications

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

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

Quasiperiodic quantum heat engines with a mobility edge

Anomalous transport through algebraically localized states in one dimension

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