Dynamical classification of topological quantum phases

Zhang, Lin; Zhang, Long; Niu, Sen; Liu, Xiong-Jun

doi:10.1016/j.scib.2018.09.018

Cited by 145 publications

(180 citation statements)

References 52 publications

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“…Detecting topological invariants plays an important role in characterizing topological states. In Hermitian systems, the winding number (or Zak phase) has been directly measured by the mean chiral displacement in photonic quantum walks [33,34] and the Ramsey interferometry of cold atoms in superlattices [35]; The Chern number has been detected via the Hall response [36,37], the Thouless pumping [38,39], the Berry curvature [40], the spin polarization [41,42], the linking number [43,44] and the emerging ring structure in quenched dynamics [7]. However, several measurement approaches succeed in Hermitian systems fail in non-Hermitian systems.…”

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confidence: 99%

Dynamic winding number for exploring band topology

Zhu

Zhong

et al. 2020

Phys. Rev. Research

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Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in both Hermitian and non-Hermitian systems via a unified approach. Here, we put forward a dynamic winding number, the winding of realistic observables in long-time average, for exploring band topology in generic two-band models. We build a concrete relation between dynamic winding numbers and equilibrium topological invariants. In one dimension, the dynamical winding number directly gives the conventional winding number. In two dimension, the Chern number relates to the weighted sum of dynamic winding numbers of all phase singularity points, in which the weight is +1 for the north pole and −1 for the south pole. This work opens a new avenue to detecting topological aspects of both Hermitian and non-Hermitian systems via general dynamic evolution.

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confidence: 99%

Dynamic winding number for exploring band topology

Zhu

Zhong

et al. 2020

Phys. Rev. Research

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“…Recently, theoretical progress has been made in generalising notions of topology to this setting. This includes studying periodically driven Hamiltonians, whose Floquet eigenstates can be topologically characterised [15][16][17][18][19][20], as well as identifying fingerprints of static topological phases in quench dynamics [21][22][23][24][25][26]. In addition to these works, which describe features of the system's trajectory over time, the instantaneous topological properties of wavefunctions undergoing time evolution have also been (a) -Equilibrium [27,28].…”

Section: Introductionmentioning

confidence: 99%

Interacting symmetry-protected topological phases out of equilibrium

McGinley

Cooper

2019

Phys. Rev. Research

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We show that the dynamics of generic isolated quantum systems admits a topological classification which captures universal features of many-body wavefunctions far from equilibrium. Specifically, we consider two short-ranged entangled wavefunctions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. By analogy to the classification of symmetry-protected topological phases, we consider the projective action of the symmetry group on a time-evolved wavefunction to explicitly calculate this nonequilibrium topological classification, focussing on systems of strongly interacting bosons in a variety of symmetry classes. The physical consequences of the non-equilibrium classification are described. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the non-equilibrium classification. arXiv:1908.06875v1 [cond-mat.str-el]

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“…Unlike the scheme in Ref. [33], which employs the quench along a single (pseudo)spin axis but measures spin polarizations in all directions to extract the topology, an alternative dynamical classification scheme was further introduced to simplify the measurement [34]. In this scheme, the topology was proposed to be characterized by topological charges, which can be precisely detected by measuring only a single spin component after a sequence of quenches along all spin quantization axes [34].…”

Section: Introductionmentioning

confidence: 99%

“…Previous schemes [33,34] have mainly considered deep quenches, which initialize a completely polarized trivial state and induces non-equilibrium dynamics by quenching the system to a topologically nontrivial phase. In this work, we extend the non-equilibrium characterization theory to the more generic case that the quench starts from a generic trivial phase with incomplete polarization, and predict interesting new physics.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, the quenchinduced evolution may carry the information of the topology of the post-quench phase. In particular, a novel dynamical bulk-surface correspondence was proven recently and applies to the generic d-dimensional (dD) topological phase [33], showing that the equilibrium bulk topology for a generic dD topological phase universally corresponds to the dynamical topology emerging in (d − 1)D momentum subspaces, dubbed band inversion surfaces (BISs). Similar to the bulk-boundary correspondence for equilibrium topological phases in the real space, the dynamical bulk-surface correspondence is of broad applicability and opens up generic non-equilibrium characterization or classification for topological phases [34][35][36][37][38][39], with novel experimental progresses having been made recently [40][41][42][43][44].Building on the dynamical bulk-surface correspon-arXiv:1907.08840v2 [cond-mat.mes-hall]…”

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confidence: 99%

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Characterizing topological phases by quantum quenches: A general theory

Zhang

Liu

2019

Phys. Rev. A

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We investigate a generic dynamical theory to characterize topological quantum phases by quantum quenches, and study the emergent topology of quantum dynamics when the quenches start from a deep or shallow trivial phase to topological regimes. Two dynamical schemes are examined: One is to characterize topological phases via quantum dynamics induced by a single quench along an arbitrary axis, and the other applies a sequence of quenches with respect to all (pseudo)spin axes. These two schemes are both built on the so-called dynamical bulk-surface correspondence, which shows that the d-dimensional (dD) topological phases with integer invariants can be characterized by the dynamical topological pattern emerging on (d − 1)D band inversion surfaces (BISs). We show that the first dynamical scheme works for both deep and shallow quenches, the latter of which is initialized in an incompletely polarized trivial phase. For the second scheme, however, when the initial phase for the quench study varies from the deep trivial (fully polarized) regime to shallow trivial (incompletely polarized) regime, a new dynamical topological transition, associated with topological charges crossing BISs, is predicted in quench dynamics. A generic criterion of the dynamical topological transition is precisely obtained. Above the criterion (deep quench regime), quantum dynamics on BISs can well characterize the topology of the post-quench Hamiltonian. Below the criterion (shallow quench regime), the quench dynamics may depict a new dynamical topology; the post-quench topology can be characterized by the emergent topological invariant plus the total charges moving outside the region enclosed by BISs. We illustrate our results by numerically calculating the 2D quantum anomalous Hall model, which has been realized in ultracold atoms. This work broadens the way to classify topological phases by non-equilibrium quantum dynamics, and has feasibility for experimental realization. † Correspondence author: xiongjunliu@pku.edu.cn * These authors contribute equally to this work. cold atoms also facilitates the study of non-equilibrium quantum dynamics in topological phases by quantum quenches [23][24][25][26][27][28]. For Chern insulators, the unitary evolution after quench does not change the topology of the many-body state. Accordingly, if the system is initialized in the trivial phase, the many-body state keeps in the trivial phase during the unitary evolution even when the post-quench target phase is topologically nontrivial [29][30][31][32]. This implies that the bulk-boundary correspondence for the equilibrium topological phases may not be satisfied in the dynamical regime. Nevertheless, the quenchinduced evolution may carry the information of the topology of the post-quench phase. In particular, a novel dynamical bulk-surface correspondence was proven recently and applies to the generic d-dimensional (dD) topological phase [33], showing that the equilibrium bulk topology for a generic dD topological phase universally corresponds to the dynamical t...

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Dynamical classification of topological quantum phases

Cited by 145 publications

References 52 publications

Dynamic winding number for exploring band topology

Dynamic winding number for exploring band topology

Interacting symmetry-protected topological phases out of equilibrium

Characterizing topological phases by quantum quenches: A general theory

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