Cornering the universal shape of fluctuations

Estienne, Benoit; Stéphan, Jean-Marie; Witczak-Krempa, William

doi:10.48550/arxiv.2102.06223

Cited by 4 publications

(7 citation statements)

References 34 publications

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“…This reproduces the expansion (27) found in the integer QHE-of course with different coefficients a n , b n , c n . FCS and symmetry-resolved entropies therefore behave in the same way as what was described in Secs.…”

Section: B Corrections To the Conformal Spectrumsupporting

confidence: 81%

“…The approximation becomes more accurate as L grows, save for the divergence at α = ±π (corresponding to Z1(±π) = 0 when Φ = 0) that cannot be captured by the integral (26). Around its maximum at α = 0, log Z1(α) behaves as a concave parabola, eventually giving the near-Gaussian behavior (27). See also Fig.…”

Section: Exact Charged Momentsmentioning

confidence: 99%

“…The charged moment (25) and its approximations (26)- (27) provide direct access to the probability distribution (8) of charge fluctuations. Indeed, assuming q = O( √ L), the Fourier transform (7) applied to the exponential (27) readily yields the large L expansion…”

Section: B Full Counting Statisticsmentioning

confidence: 99%

“…It captures e.g. the Luttinger parameter of 1D systems [14,24,25], detects and counts massless Dirac fermions in 2D [26], and measures the long-wavelength limit of the structure factor of gapped 2D liquids [27]. It was recently realized that internal symmetries also provide a natural decomposition of entanglement measures in sectors with definite values of the corresponding charge [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Equipartition of Entanglement in Quantum Hall States

Oblak,

Regnault,

Estienne

2021

Preprint

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We study the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. For the filled lowest Landau level of spin-polarized electrons on an infinite cylinder, we compute exactly the charged moments associated with a cut orthogonal to the cylinder's axis. This yields the behavior of FCS and entropies in the limit of large perimeters: in a suitable range of fluctuations, FCS is Gaussian and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections to equipartition are also derived. We then extend the analysis to Laughlin wavefunctions, where entanglement spectroscopy is carried out assuming the Li-Haldane conjecture. The results confirm equipartition up to small charge-dependent terms, and are then matched with numerical computations based on exact matrix product states.

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Section: B Corrections To the Conformal Spectrumsupporting

confidence: 81%

Section: Exact Charged Momentsmentioning

confidence: 99%

Section: B Full Counting Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Equipartition of Entanglement in Quantum Hall States

Oblak,

Regnault,

Estienne

2021

Preprint

Self Cite

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“…The universal logarithmic correction, which translates into a power law 𝑙 𝑠 in | 𝑋 𝑀 |, originates from sharp corners of the region. In general 𝑠 is a universal function of both 𝜃 and the opening angle(s) of the corners (all 𝜋/2 in this case) [25,32]. Similar corner contributions were known to arise for Rényi entropy in a CFT [33], which can be understood as the disorder operator of the replica symmetry.…”

Section: (B) the Hamiltonian Readsmentioning

confidence: 52%

Scaling of disorder operator at deconfined quantum criticality

Wang¹,

Ma²,

Cheng³

et al. 2021

Preprint

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We study the scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)𝑑 in the 𝐽-𝑄 3 model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.

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Universal signatures of Dirac fermions in entanglement and charge fluctuations

Crépel,

Hackenbroich,

Regnault

et al. 2021

Preprint

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We investigate the entanglement entropy (EE) and charge fluctuations in models where the low energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, i.e., independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and number of Dirac cones, and either for strictly two-dimensional models or for gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides non-universal, geometry dependent results.

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Cornering the universal shape of fluctuations

Cited by 4 publications

References 34 publications

Equipartition of Entanglement in Quantum Hall States

Equipartition of Entanglement in Quantum Hall States

Scaling of disorder operator at deconfined quantum criticality

Universal signatures of Dirac fermions in entanglement and charge fluctuations

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