Universal entanglement of singular surfaces

Bueno, Pablo; Myers, Robert C.; Witczak-Krempa, William

doi:10.1002/prop.201500072

Cited by 6 publications

(14 citation statements)

References 36 publications

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“…3 shows that the bounds on σ (p≤3) are comfortably satisfied. In addition, we have verified that these coefficients lie close to the coefficients of the closed-form approximate form for a E (θ) that we have previously derived, 50 which is further support for the latter.…”

Section: (Iv2)supporting

confidence: 86%

“…As pointed out in Ref. 50, this is the simplest θ-dependence compatible with the expected behavior in the limits θ → 0, π, 83 and with the reflection property of pure states, a(2π −θ) = a(θ). The smooth limit expansion coefficients, Eq.…”

supporting

confidence: 79%

“…In recent works [48][49][50] (see Refs. 8 and 51 for brief reviews), the leading order coefficient in the smooth limit, σ n , has been studied in detail, and strong evidence [48][49][50][52][53][54][55][56] points to the simple relation:…”

Section: 33mentioning

confidence: 99%

“…50,57,58 This is a line operator in d = 3, as it has support on the entangling surface, i.e., the boundary of the entangling region V . It is closely related to the swap operator used to compute the Rényi entropies with quantum Monte Carlo.…”

Section: 33mentioning

confidence: 99%

“…(I.5) and (I.6), have also been generalized to CFTs in higher dimensions. 50,60 In the presence of a (hyper)conical singularity in the entangling surface ∂V , the Rényi entropy contains an analogous regulatorindependent contribution characterized by a function of the cone opening angle, a (d) n , whose smooth limit expansion is analogous to (I.4). The leading coefficient of such an expansion has been argued to be σ…”

Section: 33mentioning

confidence: 99%

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Bounds on corner entanglement in quantum critical states

Bueno

Witczak-Krempa

2016

Phys. Rev. B

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The entanglement entropy in many gapless quantum systems receives a contribution from corners in the entangling surface in 2+1d. It is characterized by a universal function a(θ) depending on the opening angle θ, and contains pertinent low energy information. For conformal field theories (CFTs), the leading expansion coefficient in the smooth limit θ → π yields the stress tensor 2-point function coefficient CT . Little is known about a(θ) beyond that limit. Here, we show that the next term in the smooth limit expansion contains information beyond the 2-and 3-point correlators of the stress tensor. We conjecture that it encodes 4-point data, making it much richer. Further, we establish strong constraints on this and higher order smooth-limit coefficients. We also show that a(θ) is lowerbounded by a non-trivial function multiplied by the central charge CT , e.g. a(π/2) ≥ (π 2 log 2)CT /6. This bound for 90-degree corners is nearly saturated by all known results, including recent numerics for the interacting Wilson-Fisher quantum critical points (QCPs). A bound is also given for the Rényi entropies. We illustrate our findings using O(N ) QCPs, free boson and Dirac fermion CFTs, strongly coupled holographic ones, and other models. Exact results are also given for Lifshitz quantum critical points, and for conical singularities in 3+1d.

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Section: (Iv2)supporting

confidence: 86%

supporting

confidence: 79%

Section: 33mentioning

confidence: 99%

Section: 33mentioning

confidence: 99%

Section: 33mentioning

confidence: 99%

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Bounds on corner entanglement in quantum critical states

Bueno

Witczak-Krempa

2016

Phys. Rev. B

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On the Holographic Entanglement Entropy for Non‐smooth Entangling Curves in AdS₄

Pastras

2018

Fortschritte der Physik

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We extend the calculations of holographic entanglement entropy in AdS 4 for entangling curves with singular non-smooth points that generalize cusps. Our calculations are based on minimal surfaces that correspond to elliptic solutions of the corresponding Pohlmeyer reduced system. For these minimal surfaces, the entangling curve contains singular points that are not cusps, but the joint point of two logarithmic spirals one being the rotation of the other by a given angle δϕ. It turns out that, similarly to the case of cusps, the entanglement entropy contains a logarithmic term, which is absent when the entangling curve is smooth. The latter depends solely on the geometry of the singular points and not on the global characteristics of the entangling curve. The results suggest that a careful definition of the geometric characteristic of such a singular point that determines the logarithmic term is required, which does not always coincide with the definition of the angle. Furthermore, it is shown that the smoothness of the dependence of the logarithmic terms on this characteristic is not in general guaranteed, depending on the uniqueness of the minimal surface for the given entangling curve.where L 0 is some characteristic scale of the entangling curve. The linear term is the "area law", in this case a "length law", since the entangling surface is a one-dimensional closed curve, whereas

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Entanglement negativity in a two dimensional harmonic lattice: area law and corner contributions

2016

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Abstract. We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidences that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the Rényi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the Rényi entropy of order 1/2. arXiv:1604.02609v2 [cond-mat.stat-mech]

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Universal entanglement of singular surfaces

Cited by 6 publications

References 36 publications

Bounds on corner entanglement in quantum critical states

Bounds on corner entanglement in quantum critical states

On the Holographic Entanglement Entropy for Non‐smooth Entangling Curves in AdS₄

Entanglement negativity in a two dimensional harmonic lattice: area law and corner contributions

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Universal entanglement of singular surfaces

Cited by 6 publications

References 36 publications

Bounds on corner entanglement in quantum critical states

Bounds on corner entanglement in quantum critical states

On the Holographic Entanglement Entropy for Non‐smooth Entangling Curves in AdS4

Entanglement negativity in a two dimensional harmonic lattice: area law and corner contributions

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On the Holographic Entanglement Entropy for Non‐smooth Entangling Curves in AdS₄