We show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.
We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in twodimensional periodically driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time evolution of wave packets on the edge of the system. We consider the optimal driving regime for experimentally observing the Floquet topological Anderson insulator, and discuss its possible realization in photonic lattices. DOI: 10.1103/PhysRevLett.114.056801 PACS numbers: 73.20.-r, 03.65.Vf, 71.10.Pm, 71.23.An Topological states have been an ongoing fascination in condensed matter and recently led to the prediction [1][2][3] and realization [4][5][6] of various topological phases, including topological insulators (TIs). TIs possess extraordinary properties (gapless edge states [7,8], topological excitations [9]) and have a myriad of potential applications from spintronics to topological quantum computation [10]. One method to generate topological states is via periodic driving of a topologically trivial system out of equilibrium. These so-called Floquet topological insulators (FTIs) might be obtained by irradiating ordinary semiconductors with a spin-orbit interaction [11,12], or graphenelike systems [13][14][15][16]; analogues in superconducting systems have also been proposed [17,18]. Topological phases thus obtained introduce new parameters for controlling the phase, such as the frequency and intensity of the drive. Also, while FTIs have gapless edge states (just as topological insulators do), they exhibit phases with no analog in equilibrium systems [19,20]. Remarkably, topological Floquet spectra were recently experimentally realized in artificial photonic lattices where edge transport was observed [21], as well as in the solid state [22]. The tunability of photonic systems is conducive to exploring a variety of effects, including the influence of controlled disorder.Here, we are interested in the interplay of disorder and topological behavior. In two-dimensional TIs, it has been shown [23] that ballistic edge modes are robust to disorder as long as there is a bulk mobility gap. In contrast, disorder completely localizes the states of trivial noninteracting (and spinless) 2D systems. In the presence of strong spin-orbit coupling, however, disorder can induce a phase transition from a trivial to a topological Anderson insulator (TAI) phase, which exhibits quantized conductance at finite disorder strengths. TAIs were predicted in electronic models [24-27], but have not been observed experimentally.Can disorder induce topological phases in trivial periodically driven systems? Naively, we would think that disorder would destroy the conditions that give rise to Floquet topological phases. Nevertheless,...
The hallmark property of two-dimensional topological insulators is robustness of quantized electronic transport of charge and energy against disorder in the underlying lattice. That robustness arises from the fact that, in the topological bandgap, such transport can occur only along the edge states, which are immune to backscattering owing to topological protection. However, for sufficiently strong disorder, this bandgap closes and the system as a whole becomes topologically trivial: all states are localized and all transport vanishes in accordance with Anderson localization. The recent suggestion that the reverse transition can occur was therefore surprising. In so-called topological Anderson insulators, it has been predicted that the emergence of protected edge states and quantized transport can be induced, rather than inhibited, by the addition of sufficient disorder to a topologically trivial insulator. Here we report the experimental demonstration of a photonic topological Anderson insulator. Our experiments are carried out in an array of helical evanescently coupled waveguides in a honeycomb geometry with detuned sublattices. Adding on-site disorder in the form of random variations in the refractive index of the waveguides drives the system from a trivial phase into a topological one. This manifestation of topological Anderson insulator physics shows experimentally that disorder can enhance transport rather than arrest it.
We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/r α ) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench and the Fourier spectrum of these order parameters can be expolited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement, and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of onepoint observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.Long-range interacting quantum systems occur naturally in numerous quantum simulators [1][2][3][4][5][6][7][8][9][10]. A paradigmatic model considers interactions decaying with distance r as a power law 1/r α . This describes the interaction term in trappedion spin systems [3,[11][12][13][14][15], polar molecules [16][17][18][19], magnetic atoms [5,20,21], and Rydberg atoms [1,2,22,23]. One remarkable consequence of long-range interactions is the breakdown of locality, where quantum information, bounded by linear 'light cones' in short-range interacting systems [24], can propagate super-ballistically or even instantaneously [25][26][27][28][29][30]. Lieb-Robinson linear light cones have been generalized to logarithmic and polynomial light cones for long-range interacting systems [25,26,31], and non-local propagation of quantum correlations in one-dimensional (1D) spin chains has been observed in trapped-ion experiments [12,13]. Moreover, 1D long-range interacting quantum spin chains can host novel physics that is absent in their short-range counterparts, such as continuous symmetry breaking [32,33].More recently, it has been shown that confinement-which has origins in high-energy physics-has dramatic signatures in the quantum quench dynamics of short-range interacting spin chains [34]. Owing to confinement, quarks cannot be directly observed in nature as they form mesons and baryons due to strong interactions [35,36]. An archetypal model with analogous confinement effects in quantum many-body systems is the 1D short-range interacting Ising model with both transverse and longitudinal fields [37][38][39][40][41][42]. For a vanishing longitudinal field, domain-wall quasiparticles propagate freely and map out light-cone spreading of quantum information [41][42][43][44]. As first proposed by , a nonzero longitudinal field induces an attractive linear potential between two domain walls and confines them into mesonic bound quasiparticles. Recently, Kormos et al. investigated the effect of these bound states on quench dynamics and showed that the non...
where k n = 2π L (n + 1/2) with n = 0, 1, . . . , L/2 − 1.
Topological phases supporting non-Abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-Abelian anyonic chains based on the quantum groups SU͑2͒ k , a hierarchy that includes the =5/ 2 fractional quantum Hall state and the proposed =12/ 5 Fibonacci state, among others. We find that for odd k these anyonic chains realize infinite-randomness critical phases in the same universality class as the S k permutation symmetric multicritical points of Damle and Huse ͓Phys. Rev. Lett. 89, 277203 ͑2002͔͒. Indeed, we show that the pertinent subspace of these anyonic chains actually sits inside the Z k ʚ S k symmetric sector of the Damle-Huse model, and this Z k symmetry stabilizes the phase.
Conventional wisdom suggests that the long-time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal-entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy nonthermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit nonthermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have nonthermal average doublon densities. We show that this nonthermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.
We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/r α . Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α > D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α > 2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.
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