Entanglement entropy and twist fields

Caraglio, Michele; Gliozzi, F.

doi:10.1088/1126-6708/2008/11/076

Cited by 135 publications

(220 citation statements)

References 51 publications

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“…on the infinite line whose endpoints are ordered as u 1 < v 1 < u 2 < v 2 , the moments Trρ [5,14,15,12,13]. Global conformal invariance allows to write Trρ n A as follows (hereafter we will drop the dependence on the UV cutoff a)…”

Section: Review Of the Cft Resultsmentioning

confidence: 99%

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Spin structures and entanglement of two disjoint intervals in conformal field theories

Coser¹,

Tonni²,

Calabrese³

2016

J. Stat. Mech.

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Abstract. We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two or four Gaussian matrices and hence their moments can be reconstructed as computable sums of products of Gaussian operators. We find that, in the scaling limit, each term in these sums is in one-to-one correspondence with the partition function of the corresponding conformal field theory on the underlying Riemann surface with a given spin structure. The analytical findings have been checked against numerical results for the Ising chain and for the XX spin chain at the critical point. arXiv:1511.08328v1 [cond-mat.stat-mech] 26 Nov 2015Spin structures and entanglement of two disjoint intervals in CFT 2

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Section: Review Of the Cft Resultsmentioning

confidence: 99%

“…By using that P A 2 a α j P A 2 gives either −a α j or a α j , depending on whether j ∈ A 2 or j / ∈ A 2 respectively, for (14) one finds that…”

Section: Moments Of the Reduced Density Matrixmentioning

confidence: 99%

Spin structures and entanglement of two disjoint intervals in conformal field theories

Coser¹,

Tonni²,

Calabrese³

2016

J. Stat. Mech.

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“…where the four-point ratio reads 5) and x ∈ (0, 1). Since Trρ A = 1 holds, F 2,1 (x) = 1 identically.…”

Section: Mutual Informationmentioning

confidence: 99%

“…The global conformal invariance allows us to write Trρ n A for N disjoint intervals as follows [4] 5) where i, j = 1, . .…”

Section: Three Disjoint Intervalsmentioning

confidence: 99%

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Nobili¹,

Coser²,

Tonni³

2015

J. Stat. Mech.

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Abstract. The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.arXiv:1501.04311v1 [cond-mat.stat-mech]

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“…In these cases, one can construct combinations of entanglement entropies which are finite as ε → 0: the simplest case is the mutual information I A 1 ,A 2 ≡ S A 1 + S A 2 − S A 1 ∪A 2 when A = A 1 ∪ A 2 . For two dimensional CFTs, the mutual information or its generalizations to more than two intervals encode all the CFT data of the model [38][39][40][41][42][43][44][45][46]. Some results for the mutual information are also known in 2 + 1 dimensions from the quantum field theory point of view, where the analysis is more difficult because of the non local nature of ∂A [47][48][49][50][51][52].…”

Section: Jhep12(2015)037 1 Introductionmentioning

confidence: 99%

On shape dependence of holographic entanglement entropy in AdS4/CFT3

Fonda

Seminara

Tonni

2015

J. High Energ. Phys.

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Abstract:We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS 4 , asymptotically AdS 4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS 4 , the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS 4 , the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.

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Entanglement entropy and twist fields

Cited by 135 publications

References 51 publications

Spin structures and entanglement of two disjoint intervals in conformal field theories

Spin structures and entanglement of two disjoint intervals in conformal field theories

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

On shape dependence of holographic entanglement entropy in AdS4/CFT3

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