Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices

Liu, Tong; Guo, Hao; Pu, Yong; Longhi, Stefano

doi:10.1103/physrevb.102.024205

Cited by 117 publications

(84 citation statements)

References 86 publications

(96 reference statements)

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“…Recently, fresh and new perspectives on spectral localization, transport, and topological phase transitions have been disclosed in non-Hermitian lattices, where complex on-site potentials or asymmetric hopping are phenomenologically introduced to describe system interaction with the surrounding environment [29,. In particular, the interplay of aperiodic order and non-Hermiticity has been investigated in several recent works [62][63][64][65][66][67][68][69][70][71][72][73][74], revealing that the phase transition of eigenstates, from exponentially localized to extended (under periodic boundary conditions), can be often related to the change of topological (winding) numbers of the energy spectrum [55,64,72]. However, the dynamical behavior of the system near the phase transition, probed by the diffusion exponent or propagation speed of excitation, remains so far largely unexplored.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in a non-Hermitian Aubry-André-Harper model

Longhi

2021

Phys. Rev. B

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The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value V c of the quasiperiodic potential amplitude V . In terms of the dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent δ of wave-packet spreading, with δ = 1 in the delocalized phase V < V c (ballistic transport), δ 1/2 at the critical point V = V c (diffusive transport), and δ = 0 in the localized phase V > V c (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed v(V ) of excitation transport in the lattice, which is a continuous function of potential amplitude V and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-André-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous, not only in the diffusion exponent δ, but also in the speed v of ballistic transport. This means that even very close to the spectral phase transition point, rather counterintuitively, ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as V is increased above zero, i.e., surprisingly, disorder in the lattice can result in an enhancement of transport.

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Section: Introductionmentioning

confidence: 99%

Phase transitions in a non-Hermitian Aubry-André-Harper model

Longhi

2021

Phys. Rev. B

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“…So far, there are still some challenges waiting to be solved, such as the realization of TES in the visible range, more compact devices with less loss. Furthermore, in recent years, topological photonics has extended to nonlinearity (Lan et al, 2020;Xia et al, 2020), non-Hermitian (Martinez Alvarez et al, 2018Pan et al, 2018;Höckendorf et al, 2019;Liu et al, 2020;Xia et al, 2021), and synthetic dimension scales (Lin et al, 2016;Lu et al, 2021;Ni and Alù, 2021); it is worth trying to implement them based on MO effects.…”

Section: Discussion and Perspectivementioning

confidence: 99%

Magnetic-Optic Effect-Based Topological State: Realization and Application

et al. 2022

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The topological state in photonics was first realized based on the magnetic-optic (MO) effect and developed rapidly in recent years. This review summarizes various topological states. First, the conventional topological chiral edge states, which are accomplished in periodic and aperiodic systems based on the MO effect, are introduced. Some typical novel topological states, including valley-dependent edge states, helical edge states, antichiral edge states, and multimode edge states with large Chern numbers in two-dimensional and Weyl points three-dimensional spaces, have been introduced. The manifest point of these topological states is the wide range of applications in wave propagation and manipulation, to name a few, one-way waveguides, isolator, slow light, and nonreciprocal Goos–Hänchen shift. This review can bring comprehensive physical insights into the topological states based on the MO effect and provides reference mechanisms for light one-way transmission and light control.

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“…The AA model is, however, characterized by a special self-dual symmetry, which prevents the existence of a ME, and all the states in the spectrum suddenly change from extended to localized at the critical point [39][40][41][42][43]. Such features persist even when considering some non-Hermitian extensions [44][45][46][47]. Another widely studied case is the Maryland model, in which the quasiperiodic potential is unbounded [48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Anomalous mobility edges in one-dimensional quasiperiodic models

et al. 2022

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Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate energy intervals where all states are localized from energy intervals where all states are critical in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite energy interval where all states are critical. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.

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Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices

Cited by 117 publications

References 86 publications

Phase transitions in a non-Hermitian Aubry-André-Harper model

Phase transitions in a non-Hermitian Aubry-André-Harper model

Magnetic-Optic Effect-Based Topological State: Realization and Application

Anomalous mobility edges in one-dimensional quasiperiodic models

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