Tenfold Way for Quadratic Lindbladians

Lieu, Samuel N. C.; McGinley, Max; Cooper, N. R.

doi:10.1103/physrevlett.124.040401

Cited by 166 publications

(129 citation statements)

References 46 publications

(67 reference statements)

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“…Blended orbitals clearly offer novel possibilities not yet fully explored. Moreover, such blended nonbonding orbitals seem to be what is described [ 36–38 ] in the physics literature as “topological insulators,” which nevertheless conduct along the boundary, and to be, [ 91–97 ] a “topologically protected” feature (see also, refs. [62,65]).…”

Section: Edge States On Translationally Symmetric Graphene Boundariesmentioning

confidence: 99%

Conjugated‐carbon nanostructures: Emergences

Klein

Ortiz

Bytautas

2020

Int J of Quantum Chemistry

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General emergent features of conjugated-carbon nanostructures are sought. Here, "general" indicates applicability over a broad class of such structures, including graphene and buckytubes, possibly with boundaries or other sorts of defects or decorations, or rather general substructures of graphene or of buckytubes. In addition, "emergent" means that different characteristics and properties are novel and are evidenced from different models, for example, from resonance theory and Hückel theory, preferably with evidence that the features persist upon elaboration. One robust emergent feature is "Dirac cones" in the band structure of graphene and some related materials. Another interesting feature is novel "blended" boundary orbitals that are delocalized longitudinally along the boundary direction while being variably localized in the transverse direction. Furthermore, defects at the ends of polymer chains may be localized or delocalized depending on local features-although the ideas apply more widely to different conjugated-carbon structures including molecules. Explicit formulas are derived to elucidate the asymptotic behavior of unpaired electron density at the ends of selected benzenoid polymers and its relation to the associated HOMO-LUMO gap. Our approach offers a general framework to understand ab initio results, which may, at first sight, appear to be unconventional or counterintuitive to some common ideas of bonding patterns in conjugated carbon nanostructures. K E Y W O R D S carbon nanostructures, electronic structure for conjugated carbon nanostructures, graphene 1 | INTRODUCTION The human use of conjugated-carbon nanostructures predates recorded history, with coal, charcoal, and peat used as fuels or as feedstock for colorants. Within the last two centuries, different benzenoids (often derived from coal) played an important role in the industrial revolution, providing feedstocks, dyes, plastics, and drugs, and also played a central role in the development of organic chemistry and the general idea of molecular structure.

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Section: Edge States On Translationally Symmetric Graphene Boundariesmentioning

confidence: 99%

Conjugated‐carbon nanostructures: Emergences

Klein

Ortiz

Bytautas

2020

Int J of Quantum Chemistry

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“…where H 0 is the Hermitian Hamiltonian of the system; for the short-time dynamics before the occurrence of a jump of the states by Lindblad operators, one can see that the dynamics of the density matrix is described by the effective non-Hermitian Hamiltonian H eff . Recently, it was pointed out that, for noninteracting fermions, the topological properties can survive even beyond the above special dynamics [66]. This is because the gap of the Liouvillian is maintained even when the quantum jump is taken into account.…”

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confidence: 99%

Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian

Yoshida

Kudo

Katsura

et al. 2020

Phys. Rev. Research

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Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudospin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term, which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudospin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.

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“…For example, an incoming spin-up wave is related to an outgoing spin-down wave because of T S T T −1 = S. Consequently, Eq. (5) describes reciprocity in non-Hermitian systems and is relevant, for example, in mesoscopic systems [89] and open quantum systems [90][91][92]. It is also notable that this symmetry is a variant of time-reversal symmetry and called "TRS † " in Ref.…”

Section: A Symmetry and Topologymentioning

confidence: 99%

Real spectra in non-Hermitian topological insulators

Kawabata

Sato

2020

Phys. Rev. Research

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Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate the entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical edge states exhibit oscillatory dynamics due to their nonorthogonality as a unique non-Hermitian feature.

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Tenfold Way for Quadratic Lindbladians

Cited by 166 publications

References 46 publications

Conjugated‐carbon nanostructures: Emergences

Conjugated‐carbon nanostructures: Emergences

Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian

Real spectra in non-Hermitian topological insulators

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