Numerical Calculation of the Complex Berry Phase in Non-Hermitian Systems

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

doi:10.14311/ap.2017.57.0470

Cited by 25 publications

(19 citation statements)

References 45 publications

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“…[1], an algorithm to numerically evaluate the expression is described in Ref. [20]. Note, however, that the extension of Berry phases is limited to the PT -unbroken regime and if the eigenvalues of H eff are complex, the adiabatic theorem which is used in the derivation of the complex Zak phase does not apply [37] and a Berry phase is not well-defined.…”

Section: Complex Berry Phasementioning

confidence: 99%

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

et al. 2018

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We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles, one uses Lindblad operators within the scope of Lindblad master equations, the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are PT -symmetric. From the effective theory we extract a state which has similar properties as the non-equilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillean. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

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Section: Complex Berry Phasementioning

confidence: 99%

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

et al. 2018

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“…In Hermitian systems one finds different definitions and formulations of the polarization in the literature [14][15][16][17][18][19] with different physical interpretations, like the Zak phase [20]. Their generalizations to non-Hermitian systems have only recently been considered, in particular generalizations of the Zak phase [21][22][23], and very recently of Resta's polarization [24]. Note that an invariant called "biorthogonal polarization" was also introduced for non-Hermitian systems [25,26].…”

Section: Introductionmentioning

confidence: 99%

Polarization and entanglement spectrum in non-hermitian systems

Ortega-Taberner,

Rødland,

Hermanns

2021

Preprint

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The entanglement spectrum is a useful tool to study topological phases of matter, and contains valuable information about the ground state of the system. Here, we study its properties for free non-Hermitian systems for both point-gapped and line-gapped phases. While the entanglement spectrum only retains part of the topological information in the former case, it is very similar to Hermitian systems in the latter. In particular, it not only mimics the topological edge modes, but also contains all the information about the polarization, even in systems that are not topological. Furthermore, we show that the Wilson loop is equivalent to the many-body polarization and that it reproduces the phase diagram for the system with open boundaries, despite being computed for a periodic system.

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“…However, there had been hot debate about the existence of topological phase in non-Hermitian systems until recently [2][3][4][5][6][7]. We note that Berry phase can not be directly generalized to non-Hermitian systems [8]. Some authors came with an idea that topological phase is not compatible in the PT symmetric region, where P and T are parity and time reversal operators, respectively.…”

Section: Introductionmentioning

confidence: 99%

Edge states at the interface of non-Hermitian systems

Yüce

2018

Phys. Rev. A

103

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Topological edge states appear at the interface of topologically distinct two Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider PT symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that PT symmetry is spontaneously broken at the interface during the topological phase transition. Therefore topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger (SSH) model.

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Numerical Calculation of the Complex Berry Phase in Non-Hermitian Systems

Cited by 25 publications

References 45 publications

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

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

Polarization and entanglement spectrum in non-hermitian systems

Edge states at the interface of non-Hermitian systems

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