Classification of topological insulators and superconductors out of equilibrium

McGinley, Max; Cooper, N. R.

doi:10.1103/physrevb.99.075148

Cited by 66 publications

(55 citation statements)

References 75 publications

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“…Introduction.-Topological band theory was developed to predict and explain robust features in the electronic structure of insulators and superconductors close to their ground states [1,2]. While these ideas have already found fundamental applications in quantum metrology [3] and quantum computation [4], there has been a recent effort to understand the role of topology in the dynamics of many-body systems in highly nonequilibrium environments [5][6][7][8][9][10][11][12].…”

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confidence: 99%

Tenfold Way for Quadratic Lindbladians

2020

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We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These 'quadratic Lindbladians' can be captured by a non-Hermitian single-particle matrix which describes internal dynamics as well as system-environment coupling. We show that this matrix must belong to one of ten non-Hermitian Bernard-LeClair symmetry classes which reduce to the Altland-Zirnbauer classes in the closed limit. The Lindblad spectrum admits a topological classification, which we show results in gapless edge excitations with finite lifetimes. Unlike previous studies of purely Hamiltonian or purely dissipative evolution, these topological edge modes are unconnected to the form of the steady state. We provide one-dimensional examples where the addition of dissipators can either preserve or destroy the closed classification of a model, highlighting the sensitivity of topological properties to details of the system-environment coupling.

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confidence: 99%

Tenfold Way for Quadratic Lindbladians

2020

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“…We can also make connection with our previous results on non-equilibrium classifications of free-fermion systems [29,30] using the Jordan-Wigner transform approach [44]. In that context, the fermion systems belong to one of 10 Altland-Zirnbauer symmetry classes [56], which can then be re-interpreted as symmetry groups of the auxiliary spin system (although in some cases one needs to specify whether the free Hamiltonian represents a superconductor or an insulator [57]).…”

Section: Non-equilibrium Spt Classification In 1dmentioning

confidence: 55%

“…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]. In this approach, the time dependence of non-interacting bulk indices can be understood, allowing one to systematically characterise non-interacting free fermion systems far from equilibrium [29,30]. However, the techniques applied in these previous studies are specific to non-interacting systems, and do not generalize to strongly interacting SPT phases.…”

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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“…Compared to Schemes I, which always works for an incompletely polarized state, Scheme II requires a constraint on the quench depth, i.e., on the polarization of the initial trivial phase, since various degrees of freedom are involved in the characterization. The formulas (37) and (38) imply that the criterion also depends on the system dimension.…”

Section: Discussionmentioning

confidence: 99%

“…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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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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Classification of topological insulators and superconductors out of equilibrium

Cited by 66 publications

References 75 publications

Tenfold Way for Quadratic Lindbladians

Tenfold Way for Quadratic Lindbladians

Interacting symmetry-protected topological phases out of equilibrium

Characterizing topological phases by quantum quenches: A general theory

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