scholarly journals Renormalized entanglement entropy and curvature invariants

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Marika Taylor ◽  
Linus Too
Keyword(s):  
Entanglement Entropy ◽  
Renormalization Scheme ◽  
Replica Trick ◽  
Curvature Invariants

Abstract Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces. In this paper we show how holographic renormalized entanglement entropy can be expressed in terms of the Euler invariant of the surface and renormalized curvature invariants. For a spherical entangling region in an odd-dimensional CFT, the renormalized entanglement entropy is proportional to the Euler invariant of the holographic entangling surface, with the coefficient of proportionality capturing the (renormalized) F quantity. Variations of the entanglement entropy can be expressed elegantly in terms of renormalized curvature invariants, facilitating general proofs of the first law of entanglement.

scholarly journals On the renormalization of entanglement entropy

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Jin-Yi Pang ◽  
Jiunn-Wei Chen
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Replica Trick ◽  
Dimensional Spacetime

AbstractThe renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

scholarly journals Perturbative calculations of entanglement entropy

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pouria Dadras ◽  
Alexei Kitaev
Keyword(s):  
Entanglement Entropy ◽  
Heat Bath ◽  
Initial Section ◽  
Perturbation Series ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Replica Trick ◽  
General Systems ◽  
Interesting Contribution ◽  
External Impulse

Abstract This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling κ; the most interesting contribution is of order 2s, where s is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.

scholarly journals Shape dependence of renormalized holographic entanglement entropy

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Giorgos Anastasiou ◽  
Javier Moreno ◽  
Rodrigo Olea ◽  
David Rivera-Betancour
Keyword(s):  
Lower Bound ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Renormalization Scheme ◽  
Strong Subadditivity ◽  
Shape Dependence ◽  
Holographic Entanglement Entropy ◽  
Curvature Term ◽  
Topological Part ◽  
Willmore Energy

Abstract We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even- dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS4/CFT3, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property.

scholarly journals Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Marius Gerbershagen
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Zero Point ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Replica Trick ◽  
Twist Operators

Abstract We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus.

scholarly journals Disentangling the thermofield-double state

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pouria Dadras
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Strong Coupling ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
One Dimension ◽  
Leading Order ◽  
Point Function ◽  
Replica Trick ◽  
Large N

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

scholarly journals A path integral ground state replica trick approach for the computation of entanglement entropy of dipolar linear rotors

2020 ◽  
Vol 152 (18) ◽  
pp. 184113 ◽  
Author(s):  
Tapas Sahoo ◽  
Dmitri Iouchtchenko ◽  
C. M. Herdman ◽  
Pierre-Nicholas Roy
Keyword(s):  
Path Integral ◽  
Ground State ◽  
Entanglement Entropy ◽  
Replica Trick

scholarly journals Islands in de Sitter space

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Arjun Kar ◽  
Tomonori Ugajin
Keyword(s):  
Black Hole ◽  
Entanglement Entropy ◽  
De Sitter Space ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Replica Trick ◽  
Compact Geometry ◽  
Entropy Growth ◽  
Spatial Section ◽  
Conventional Field

Abstract We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal “islands” in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Entanglement entropy in low-energy field theories at a finite chemical potential

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Ivan Morera ◽  
Irénée Frérot ◽  
Artur Polls ◽  
Bruno Juliá-Díaz
Keyword(s):  
Chemical Potential ◽  
Entanglement Entropy ◽  
Low Energy ◽  
Field Theories ◽  
Energy Field

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

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