The g-theorem and quantum information theory

Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo

doi:10.1007/jhep10(2016)140

Cited by 131 publications

(174 citation statements)

References 46 publications

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“…It also agrees with a result for an equivalent model solved in Ref. [17] based solely on free fermion techniques. Our fully analytic approach is facilitated via a bosonization scheme for the so called twist-field, an object in the field theory that realizes the n-sheeted Riemann geometry and whose correlation function encodes entanglement properties 13,24 class, such as negativity [32][33][34][35][36] or entanglement of multiple intervals [37][38][39] .…”

Section: Introductionsupporting

confidence: 90%

“…[17] for a proof of the g-theorem in the context of entanglement and Refs. [18,19] for a holographic view in the context of the Kondo effect.…”

Section: Introductionmentioning

confidence: 99%

“…1. A number of fruitful techniques had been applied to the EE in this theory, either based on its simple free fermion structure 17 , or via the form-factor approach 16,17,[24][25][26] . With an eye on possible generalizations to other theories, finding additional convenient techniques for the Ising model may be highly valuable.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

Cornfeld

Sela

2017

Phys. Rev. B

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The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g-theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g-theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an n-sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing to track in real space the presence of a region containing one half of a qubit with entropy 1 2 log(2), associated with a free local Majorana fermion.

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Section: Introductionsupporting

confidence: 90%

“…[17] for a proof of the g-theorem in the context of entanglement and Refs. [18,19] for a holographic view in the context of the Kondo effect.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

Cornfeld

Sela

2017

Phys. Rev. B

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“…We follow the steps of the recent work [19], where relative entropy was shown to lead to a simple proof of the g-theorem for d = 2 conformal field theories (CFT) in a space with a boundary at x = 0.…”

Section: Jhep03(2017)089mentioning

confidence: 99%

Relative entropy and the RG flow

Casini

Testé

Torroba

2017

J. High Energ. Phys.

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We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension ∆ of the perturbation that triggers the RG flow.

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“…The contribution from defects/impurities to the EE of a spherical region of radius R is a candidate g-function (see e.g. [31,32]) and its behaviour for the D3-brane flow solution would clearly be very interesting. It should also be possible to analyse the D3-brane system from the viewpoint of the bosonic quantum mechanics of the boundary impurity.…”

Section: Finite Temperature D3-brane Embeddingsmentioning

confidence: 99%

Holographic flows and thermodynamics of Polyakov loop impurities

Kumar

Silvani

2017

J. High Energ. Phys.

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We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N = 4 supersymmetric gauge theory. These correspond to non-conformal D3-and D5-brane probe embeddings in AdS 5 × S 5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the non-conformal, D3-brane solution interpolates between the symmetric representation in the UV and fundamental sources in the IR. The D5-brane embeddings exhibit nontrivial thermodynamics with multiple branches of solutions, whilst the thermal analogue of the interpolating D3-brane solution does not appear to exist.

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The g-theorem and quantum information theory

Cited by 131 publications

References 46 publications

Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

Relative entropy and the RG flow

Holographic flows and thermodynamics of Polyakov loop impurities

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