Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians

Araki, Hiromu; Fukui, Tsuguya; Hatsugai, Yasuhiro

doi:10.1103/physrevb.96.165139

Cited by 8 publications

(9 citation statements)

References 61 publications

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“…x = P (13) , M y P (13) M −1 y = P (24) , M x P (14) M −1 x = P (23) , M y P (14) M −1 y = P (14) , M x P (12) M −1 x = P (34) , M y P (12) M −1 y = P (34) , (24) leads to…”

Section: B Symmetry Property Of Ep and Esmentioning

confidence: 99%

“…Finally let us briefly discuss C 4 symmetry. Note the following transformation property of P (ij) , r4 P (13) r−1 4 = P (14) , r4 P (14) r−1 4 = P (24) , r4 P (24) r−1 4 = P (23) , r4 P (23) r−1 4 = P (13) , r4 P (12) r−1 4 = P (34) , r4 P (34) r−1 4 = P (12) .…”

Section: B Symmetry Property Of Ep and Esmentioning

confidence: 99%

“…This method is based on the topological numbers of the entanglement Hamiltonian (eH). It turns out that not only the topological numbers of the original Hamiltonian, but also those of eH of subsystems are very useful to characterize the topological phases of complicated systems [33,34].…”

Section: Introductionmentioning

confidence: 99%

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Entanglement polarization for the topological quadrupole phase

Fukui

Hatsugai

2018

Phys. Rev. B

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We propose the entanglement dipole polarization to describe the topological quadrupole phase. The quadrupole moment can be regarded as a pair of the dipole moment, in which the total dipole moment is canceled. The entanglement polarization, we propose, is useful to detect such a constituent dipole polarization. We first introduce partitions of sites in the unit cell and divide the system into two subsystems. Then, introducing an entanglement Hamiltonian by tracing out one of the subsystems partly, we compute the dipole polarization of the occupied states associated with the entanglement Hamiltonian, which is referred to as the entanglement polarization. Although the total dipole polarization is vanishing, those of the subsystems can be finite. The entanglement dipole polarization is quantized by reflection symmetries. We also introduce the entanglement polarization of the edge states, which reveals that the edge states themselves are gapped and topologically nontrivial. Therefore, such edge states yield the zero energy edge states if the system has boundaries. This is the origin of the corner states.

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“…x = P (13) , M y P (13) M −1 y = P (24) , M x P (14) M −1 x = P (23) , M y P (14) M −1 y = P (14) , M x P (12) M −1 x = P (34) , M y P (12) M −1 y = P (34) , (24) leads to…”

Section: B Symmetry Property Of Ep and Esmentioning

confidence: 99%

Section: B Symmetry Property Of Ep and Esmentioning

confidence: 99%

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Entanglement polarization for the topological quadrupole phase

Fukui

Hatsugai

2018

Phys. Rev. B

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“…IV for these non-Dirac systems, or to apply the techniques of the entanglement Chern number, which can separate the Chern number into those of subsystems. 69,70 .…”

Section: Summary and Discussionmentioning

confidence: 99%

Topological magnetoelectric pump in three dimensions

Fukui

Fujiwara

2017

Phys. Rev. B

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We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the $1+1$ dimensional system as well as $3+1$ dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore, the pumped particle number is quantized by the topological reason. Finally we study the topological temporal pump in $3+1$ dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.Comment: 16 pages, 8 figures; final versio

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“…In Fig. 6(c), we depict the phase diagram of this model, obtained by calculating the entanglement Chern number [55][56][57][58], enCh σ , for the lowest two bands. To be concrete, the entanglement Chern number is defined for the eigenstates of the entanglement Hamiltonian H en (k):…”

Section: Molecular-orbital Kane-mele Modelmentioning

confidence: 99%

Systematic construction of topological flat-band models by molecular-orbital representation

Mizoguchi,

Hatsugai

2020

Preprint

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On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models, the topological natures are encoded not into the flat band itself but into the dispersive bands touched with the flat band. Such a band structure may become a source of exotic phenomena arising from the combination of flat bands, topology and correlations.

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Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians

Cited by 8 publications

References 61 publications

Entanglement polarization for the topological quadrupole phase

Entanglement polarization for the topological quadrupole phase

Topological magnetoelectric pump in three dimensions

Systematic construction of topological flat-band models by molecular-orbital representation

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