Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model

Dangel, Felix; Wagner, M.; Cartarius, Holger; Main, Jörg; Wunner, Günter

doi:10.1103/physreva.98.013628

Cited by 94 publications

(61 citation statements)

References 42 publications

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“…One can similarly show that the same holds for the case of pure gain and for separate loss and gain channels on each site. The authors of [36] found a similar result for a dissipative SSH model, in which the topological band structure of the Liouvillian was identical to that of the Hamiltonian.…”

Section: Topological Properties Of X(k)mentioning

confidence: 60%

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

2019

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We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad gen-eratorL of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -localized eigenmodes ofL. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current. Contents arXiv:1812.02126v2 [cond-mat.str-el] 25 Jan 2019 SciPost Physics Submission 4.2 Lindblad-Floquet theory 15 4.3 Numerical results 16 5 Conclusions and outlook 20 References 21 A Geometric interpretation of the winding number 25 B Computing the winding number 25 C Topology of X vs. A 26 D Edge modes of X 27 E Time evolution of observables 28 F Off-diagonal Floquet blocks and their importance 29

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Section: Topological Properties Of X(k)mentioning

confidence: 60%

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

2019

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“…We note that Berry phases for non-Hermitian systems are defined in several contexts [129,130]. However, it remains unsolved whether there exists a topological invariant that characterizes the topological properties even in the presence of the jump term.…”

Section: B Properties Of the Berry Phase χ Knmentioning

confidence: 97%

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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“…In Fig. 2, we present two examples of the winding numbers (ν 0 , ν π ) versus the imaginary parts of hopping amplitudes v 1 = v 2 = v in our PQL model (25). In both cases, we observe that the topological invariants ν 0 (solid line) and ν π (dashed line) and their changes are consistent with the mean chiral displacements C 0 (circles) and C π (triangles), respectively (see Appendix A for the definitions of C 0,π ).…”

Section: Non-hermitian Floquet Topological Phases In a Pqlmentioning

confidence: 99%

Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

Zhou

2019

Phys. Rev. B

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Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of their topological properties. In this work, we propose a systematic approach to dynamically characterize non-Hermitian Floquet topological phases in one-dimension with chiral symmetry. We show that the topological invariants of a chiral symmetric Floquet system can be fully determined by measuring the winding angles of its time-averaged spin textures. We further purpose a piecewise quenched lattice model with rich non-Hermitian Floquet topological phases, in which our theoretical predictions are numerically demonstrated and compared with another approach utilizing the mean chiral displacement of a wavepacket.

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Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model

Cited by 94 publications

References 42 publications

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

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

Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

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