Geometric entanglement in the integer quantum Hall state at 
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 with boundaries

Rozon, Pierre-Gabriel; Bolteau, Pierre-Alexandre; Witczak-Krempa, William

doi:10.1103/physrevb.102.155417

Cited by 5 publications

(5 citation statements)

References 22 publications

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“…In the presence of edge degrees of freedom the entanglement entropy for the twodimensional integer quantum Hall effect develops subleading logarithmic contributions [6]. It has been shown in the two-dimensional ν = 1 quantum Hall effect that when the edge boundary intersects the boundary of the entangling surface there is an additional logarithmic contribution whose coefficient is determined by the central charge of the gapless edge modes [7]- [8]. In the context of higher dimensional quantum Hall effect we have previously analyzed the analogs of higher dimensional chiral abelian and nonabelian droplets, the edge spectrum and corresponding effective actions [10].…”

Section: Discussionmentioning

confidence: 99%

“…Of particular interest among two-dimensional gapped systems are the quantum Hall systems whose entanglement entropy has been widely studied under different partitions. For a real-space partition γ = 0 for fully filled integer Quantum Hall states and nonzero for fractional quantum Hall states [2]- [8]. The entanglement entropy in the case of integer quantum Hall states is amenable to analytical calculations due to the fact that the manybody ground state is in terms of free fermions.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement entropy for integer quantum Hall effect in two and higher dimensions

Karabali

2020

Preprint

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We analyze the entanglement entropy, in real space, for the higher dimensional integer quantum Hall effect on CP k (any even dimension) for abelian and nonabelian magnetic background fields. In the case of ν = 1 we perform a semiclassical calculation which gives the entropy as proportional to the phase-space area. This exhibits a certain universality in the sense that the proportionality constant is the same for any dimension and for any background, abelian or nonabelian. We also point out some distinct features in the profiles of the eigenfunctions of the two-point correlator that underline the difference in the value of entropies between ν = 1 and higher Landau levels.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entanglement entropy for integer quantum Hall effect in two and higher dimensions

Karabali

2020

Preprint

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“…The EE of skeletal regions with cusps thus displays novel scaling behavior. Indeed, as it is well-known [23][24][25][26][27][28][29][30][31][32][33], 2d regions with bulk and/or boundary corners show a loga-rithmic divergence at large in gapless critical systems.…”

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confidence: 81%

Entanglement of skeletal regions

Berthiere,

Witczak-Krempa

2021

Preprint

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The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for a subregion of finite volume (or area in 2d). In this work, we study the EE of skeletal regions that have no volume, such as a line in 2d/3d. We show that skeletal entanglement displays new behavior compared to its bulk counterpart, and leads to distinct universal quantities. We provide non-perturbative bounds for the skeletal area-law coefficient of a large family of quantum states. We then explore skeletal scaling for the toric code, conformal bosons and Dirac fermions, Lifshitz critical points, and Fermi liquids. We discover signatures including skeletal topological EE, novel bulk and boundary cusp terms, and strict area-law scaling for metals. We discuss the possibility of a continuum description involving the fusion of extended defect operators. Finally, we outline open questions relating to other systems, and measures such as the logarithmic negativity.

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“…We fit the S α (θ) [36,37] with the function S α (θ) = u α [1 + (π − θ) cot(θ)] and find that u 1 = −0.0861 (±0.0009), u 2 = −0.0613 (±0.0007) and u 3 = −0.0531 (±0.0006). In [28], the corner contribution was recently calculated in cylinder geometry. While θ → 0, it was found that the divergence of the S 1 (θ) behaves as S 1 (θ) = −0.0886 (±0.0004)/θ where the coefficient is consistent with our result of u 1 for the bulk corner.…”

Section: Corner Contributionmentioning

confidence: 99%

“…Once the boundary has a sharp corner, regardless of whether the system is gapped or not, it was found that the corner on the boundary has an important contribution in the EE which was previously explored [14-27] in two-dimensional quantum critical systems and CFT. Recently, it was extended to the gapped topological system such as the integer quantum Hall states [13,28,29]. The corner angle dependence of the EE is found to be universal [30].…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy of the quantum Hall edge and its geometric contribution

Yang²,

Li³

et al. 2022

Front. Phys.

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Generally speaking, entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short-range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in long-range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Furthermore, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. In this work, we simultaneously explore the geometric and edge contributions in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Their scaling is found to be consistent with conformal field theory (CFT) predictions and recent results of particle number fluctuation calculations.

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Geometric entanglement in the integer quantum Hall state at ν=1 with boundaries

Cited by 5 publications

References 22 publications

Entanglement entropy for integer quantum Hall effect in two and higher dimensions

Entanglement entropy for integer quantum Hall effect in two and higher dimensions

Entanglement of skeletal regions

Entanglement entropy of the quantum Hall edge and its geometric contribution

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