Holographic relations for OPE blocks in excited states

Cresswell, Jesse C.; Jardine, Ian T.; Peet, Amanda W.

doi:10.1007/jhep03(2019)058

Cited by 11 publications

(8 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is non-negative and is positive when µ is negative. Now notice that our ρ Γ B AB given by (28) can be regarded as |A| + |B| copies of this kind of quantum mechanics. Thus, finally, we can evaluate the logarithmic negativity as follows:…”

Section: Acknowledgmentsmentioning

confidence: 99%

Entanglement of Purification in Many Body Systems and Symmetry Breaking

et al. 2019

View full text Add to dashboard Cite

We study the entanglement of purification (EoP), a measure of total correlation between two subsystems A and B, for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EoP becomes a non-monotonic function of the distance between A and B when the total number of lattice sites is small. When it is large, the EoP becomes monotonic and shows a plateau-like behavior. Moreover, we show that the original reflection symmetry which exchanges A and B can get broken in optimally purified systems. In the Ising model, we find this symmetry breaking in the ferromagnetic phase. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.

show abstract

Section: Acknowledgmentsmentioning

confidence: 99%

Entanglement of Purification in Many Body Systems and Symmetry Breaking

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Also in [17][18][19], connections between E W (ρ AB ) and quantities other than the EoP have been proposed. For other recent progresses on the HEoP, refer to [20][21][22][23][24][25][26][27][28][29][30][31][32] In this letter, we would like to present a direct comparison between the HEoP E W (ρ AB ) and the entanglement entropy S AÃ for a special class of purification |Ψ AÃBB , obtained by the path-integral optimization [33,34]. We will focus on several examples in AdS 3 /CFT 2 and will find both quantities always agree with each other in the regime of validity of our computations.…”

Section: Introductionmentioning

confidence: 99%

Holographic Entanglement of Purification from Conformal Field Theories

et al. 2019

View full text Add to dashboard Cite

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples. arXiv:1812.05268v1 [hep-th]

show abstract

“…A conical defect in AdS is dual to an excited state created, via the state/operator correspondence, by a heavy operator in the CFT [61][62][63][64]. There is substantial evidence that the CFT state dual to AdS 3 /Z N is excited by an operator which, at large c, has scaling dimension [65][66][67]…”

Section: First Law Of Differential Entropy and Holographic Complexitymentioning

confidence: 99%

“…Three-dimensional spacetimes with constant negative curvature can be constructed as quotients of pure AdS 3 by a discrete subgroup of the isometry group [8,83]. In particular, a spatial section of the conical defect spacetime follows from quotienting two-dimensional hyperbolic space by the conjugacy class of its isometry group that is generated by an elliptic element, which depends on a single parameter [67,[84][85][86].…”

Section: A First Law In Adsmentioning

confidence: 99%

The first law of differential entropy and holographic complexity

Sarkar¹,

Visser²

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We construct the CFT dual of the first law of spherical causal diamonds in three-dimensional AdS spacetime. A spherically symmetric causal diamond in AdS3 is the domain of dependence of a spatial circular disk with vanishing extrinsic curvature. The bulk first law relates the variations of the area of the boundary of the disk, the spatial volume of the disk, the cosmological constant and the matter Hamiltonian. In this paper we specialize to first-order metric variations from pure AdS to the conical defect spacetime, and the bulk first law is derived following a coordinate based approach. The AdS/CFT dictionary connects the area of the boundary of the disk to the differential entropy in CFT2, and assuming the ‘complexity=volume’ conjecture, the volume of the disk is considered to be dual to the complexity of a cutoff CFT. On the CFT side we explicitly compute the differential entropy and holographic complexity for the vacuum state and the excited state dual to conical AdS using the kinematic space formalism. As a result, the boundary dual of the bulk first law relates the first-order variations of differential entropy and complexity to the variation of the scaling dimension of the excited state, which corresponds to the matter Hamiltonian variation in the bulk. We also include the variation of the central charge with associated chemical potential in the boundary first law. Finally, we comment on the boundary dual of the first law for the Wheeler-deWitt patch of AdS, and we propose an extension of our CFT first law to higher dimensions.

show abstract

Holographic relations for OPE blocks in excited states

Cited by 11 publications

References 53 publications

Entanglement of Purification in Many Body Systems and Symmetry Breaking

Entanglement of Purification in Many Body Systems and Symmetry Breaking

Holographic Entanglement of Purification from Conformal Field Theories

The first law of differential entropy and holographic complexity

Contact Info

Product

Resources

About