Quantum Dynamical Characterization and Simulation of Topological Phases With High-Order Band Inversion Surfaces

Yu, Xiang-Long; Ji, Wentao; Zhang, Lin; Wang, Ya; Wu, Jiansheng; Liu, Xiong-Jun

doi:10.1103/prxquantum.2.020320

Cited by 25 publications

(12 citation statements)

References 63 publications

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“…We begin with an introduction of the nested-BIS method for constructing and characterizing HOTPs with arbitrary orders of topology in arbitrary dimensions [34]. This method is built on the BISs and high-order BISs used to dynamically characterize the first-order topological phases, where mth-order BISs are given by a special region in the Brillouin zone with m vanishing pseudo-spin components of the Hamiltonian, denoted as m-BISs [41,42]. Following the nested-BIS method, a dD Hamiltonian hosting nth-order topology can be constructed as…”

Section: The Nested Band Inversion Surfacesmentioning

confidence: 99%

“…The starting point of this work is a method known as the nested band inversion surfaces (BISs), which has been employed to explore HOTPs in A and AIII classes of the AZ classes [34]. This method is built on the concept of BISs, which offers a powerful and innovative approach to probe 1st-order topological invariants through quantum dynamics [41][42][43]. Inhabiting this advantage, the nested-BIS method allows us to construct higher-order topology from 1st-order one of different parts of the system's Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, we extend our discussion to two scenarios beyond the standard nested-BIS method. Namely, asymmetric parameters along different directions may lead to crossed BISs, and a nested relation can only be recovered by taking into account high-order BISs [42]. Secondly, the standard nested-BIS method requires the Hamiltonian to be formed by Clifford operators [34], and a generalization of this method for systems with certain non-Clifford operators is established with extra effective surface BISs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topological classification of Higher-order topological phases with nested band inversion surfaces

Lei,

Deng,

2022

Preprint

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Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this work, we provide a unified construction and topological characterization of HOTPs for the full Altland-Zirnbauer tenfold symmetry classes, based on a method known as the nested band inversion surfaces (BISs). Specifically, HOTPs built on this method are decomposed into a series of subsystems, and higher-order topological boundary states emerges from the interplay of their 1st-order topology. Our analysis begins with a general discussion of HOTPs in continuous Hamiltonians for each symmetry class, then moves on to several lattice examples illustrating the topological characterization based on the nested-BIS method. Despite that the example minimal models possess several spatial symmetries, our method does not rely on any spatial symmetry, and can be easily extended into arbitrary orders of topology in dimensions. Furthermore, we extend our discussion to systems with asymmetric boundary states induced by two different mechanisms, namely crossed BISs that break a C4 rotation symmetry, and non-Clifford operators that break certain chiral-mirror symmetries of the minimal models.

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Section: The Nested Band Inversion Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topological classification of Higher-order topological phases with nested band inversion surfaces

Lei,

Deng,

2022

Preprint

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“…Despite the fact that topological phases are defined at the ground state at equilibrium, quantum quenches in recent studies provide nonequilibrium way to investigate topological physics [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . Particularly, as a momentum-space counterpart of the bulk-boundary correspondence, the dynamical bulksurface correspondence was proposed [29][30][31][32][33][34] , which relates the bulk topology of an equilibrium phase to nontrivial dynamical topological phase emerging on certain momentum subspaces called band-inversion surfaces (BISs) when quenching the system across topological transitions. This dynamical topology enables a broadly applicable way to characterize and detect topological phases by quantum dynamics, and has triggered many experimental studies in quantum simulations, such as in ultracold atoms 35,36 , nitrogen-vacancy defects in diamond [37][38][39] , nuclear magnetic resonance (NMR) 40 , and superconducting circuits 41 .…”

Section: Introductionmentioning

confidence: 99%

Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation

Zhang

Long

et al. 2022

npj Quantum Inf

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Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in an experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH) model using the nuclear magnetic resonance processor. Unlike the usual experiments using auxiliary qubits, we develop a stochastic average approach based on the stochastic Schrödinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifying the implementation of quantum gates. We demonstrate the stability of dynamical topology against weak noise and observe two types of dynamical topological transitions driven by strong noise. Moreover, a region where the emergent topology is always robust regardless of the noise strength is observed. Our work shows a feasible quantum simulation approach for dissipative quantum dynamics with stochastic Schrödinger equation and opens a route to investigate non-Hermitian dynamical topological physics.

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“…Introduction-Intriguing physical phenomena, such as topological phases, can emerge from symmetries, which play an important role in determining a system properties [1][2][3][4][5][6][7]. Symmetries can lead to general universality classes, so that, for example, phases of topological insulators can be arranged into a periodic table [1].…”

mentioning

confidence: 99%

Observation of symmetry-protected selection rules in periodically driven quantum systems

Wang,

Li,

Cappellaro

2021

Preprint

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Periodically driven quantum systems, known as Floquet systems, have been a focus of nonequilibrium physics in recent years, thanks to their rich dynamics. Not only time-periodic systems exhibit symmetries similar to those in spatially periodic systems, but they also display novel behavior due to symmetry breaking. Characterizing such dynamical symmetries is crucial, but the task is often challenging, due to limited driving strength and the lack of an experimentally accessible characterization protocol. Here, we show how to characterize dynamical symmetries including parity, rotation, and particle-hole symmetry by observing the symmetry-induced selection rules between Floquet states. Specifically, we exploit modulated quantum driving to reach the strong light-matter coupling regime and we introduce a protocol to experimentally extract the transition elements between Floquet states from the coherent evolution of the system. Using the nitrogen-vacancy center in diamond as an experimental testbed, we apply our methods to observe symmetry-protected dark states and dark bands, and the coherent destruction of tunneling effect. Our work shows how to exploit the quantum control toolkit to study dynamical symmetries that can arise in topological phases of strongly-driven Floquet systems.

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Quantum Dynamical Characterization and Simulation of Topological Phases With High-Order Band Inversion Surfaces

Cited by 25 publications

References 63 publications

Topological classification of Higher-order topological phases with nested band inversion surfaces

Topological classification of Higher-order topological phases with nested band inversion surfaces

Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation

Observation of symmetry-protected selection rules in periodically driven quantum systems

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