Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

Titum, Paraj; Berg, Erez; Rudner, Mark S.; Refael, Gil; Lindner, Netanel H.

doi:10.1103/physrevx.6.021013

Cited by 314 publications

(377 citation statements)

References 66 publications

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“…1(a)]. Harnessing the unique properties of periodically driven quantum systems [12][13][14][15][16][17], here we show how these limitations can be circumvented: we find perfect spin-momentum locking in the stroboscopic dynamics of a periodically driven 1D lattice model. While conventional helical edge states require a time reversal symmetric topological 2D bulk [19], the spin-momentum locking in our 1D setting stems from topological properties in combined time-momentum (Floquet) space [see Fig.…”

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confidence: 75%

Helical Floquet Channels in 1D Lattices

Budich¹,

Hu²,

Zoller³

2017

Phys. Rev. Lett.

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We show how dispersionless channels exhibiting perfect spin-momentum locking can arise in a 1D lattice model. While such spectra are forbidden by fermion doubling in static 1D systems, here we demonstrate their appearance in the stroboscopic dynamics of a periodically driven system. Remarkably, this phenomenon does not rely on any adiabatic assumptions, in contrast to the well known Thouless pump and related models of adiabatic spin pumps. The proposed setup is shown to be experimentally feasible with state of the art techniques used to control ultracold alkaline earth atoms in optical lattices.Introduction. Exploring the rich phenomenology of spin-orbit coupling is an active field of research in numerous branches of quantum physics [1][2][3]. The discovery of helical edge-states [4][5][6] has opened the route towards perfect spin-momentum locking, characterized by a oneto-one correspondence between the propagation direction of particles and their spin. Such exotic states have only been realized at the surface of 2D topological insulators [4,[7][8][9][10]. Without the 2D bulk, their occurrence is forbidden in 1D lattice systems [10], as the periodicity of band structures in the first Brillouin Zone (BZ) imposes fundamental constraints -referred to as fermion doubling [11] [cf. Fig. 1(a)]. Harnessing the unique properties of periodically driven quantum systems [12-17], here we show how these limitations can be circumvented: we find perfect spin-momentum locking in the stroboscopic dynamics of a periodically driven 1D lattice model. While conventional helical edge states require a time reversal symmetric topological 2D bulk [19], the spin-momentum locking in our 1D setting stems from topological properties in combined time-momentum (Floquet) space [see Fig. 1(d)], and relies on a spin-rotation symmetry of the stroboscopic dynamics. Our approach goes conceptually beyond adiabatically projected models such as the Thouless pump [20,21], in that we consider the full quasienergy spectrum without involving adiabatic projections.In Floquet systems, the quasi-energies are only defined modulo the driving frequency Ω, allowing for spectra that are only periodic in the BZ up to integer multiples of Ω. However, even in driven systems, unidirectional motion in 1D systems cannot be achieved without adiabatic assumptions, due to fundamental topological constraints [18]. The central result of this work is that the Floquet Bloch Hamiltonian ( = 1)

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confidence: 75%

Helical Floquet Channels in 1D Lattices

Budich¹,

Hu²,

Zoller³

2017

Phys. Rev. Lett.

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“…Such lattices, which include coherent wave networks and periodically-driven lattices, are governed by evolution matrices rather than Hamiltonians. Previous studies have shown that Floquet lattice bandstructures can host a variety of phases, including topological insulator phases with protected surface states [11][12][13][14][15][16] . Most interestingly, there exist 2D "anomalous" Floquet insulator phases that are topologically distinct from conventional insulators, despite all bands having vanishing Chern numbers 14,15,17 ; this is unique to Floquet lattices, and cannot be understood in the framework of static Hamiltonians.…”

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confidence: 99%

Floquet Weyl phases in a three-dimensional network model

2016

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We study the topological properties of 3D Floquet bandstructures, which are defined using unitary evolution matrices rather than Hamiltonians. Previously, 2D bandstructures of this sort have been shown to exhibit anomalous topological behaviors, such as topologically-nontrivial zero-Chernnumber phases. We show that the bandstructure of a 3D network model can exhibit Weyl phases, which feature "Fermi arc" surface states like those found in Weyl semimetals. Tuning the network's coupling parameters can induce transitions between Weyl phases and various topologically distinct gapped phases. We identify a connection between the topology of the gapped phases and the topology of Weyl point trajectories in k-space. The model is feasible to realize in custom electromagnetic networks, where the Weyl point trajectories can be probed by scattering parameter measurements.

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“…This approach does not rely on thermal equilibrium, and applies very naturally to time-dependent systems. It is therefore particularly suited for the identification of dynamical as well as Floquet phases [30][31][32][33][34][35][36][37][38][39].…”

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confidence: 99%

Learning phase transitions from dynamics

2018

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We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two distinct models of one-dimensional disordered and interacting spin chains. The obtained phase diagram for a well-studied model of the many-body localization transition shows excellent agreement with previously known results obtained from time-independent entanglement spectra. For a periodically driven model featuring an inherently dynamical time-crystalline phase, the phase diagram that our network traces coincides with an order parameter for its expected phases.

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Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump

Cited by 314 publications

References 66 publications

Helical Floquet Channels in 1D Lattices

Helical Floquet Channels in 1D Lattices

Floquet Weyl phases in a three-dimensional network model

Learning phase transitions from dynamics

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