scholarly journals Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
Aranya Bhattacharya ◽  
Kevin T. Grosvenor ◽  
Shibaji Roy
Keyword(s):  
Entanglement Entropy ◽  
Ads Spacetime ◽  
Thermal Perturbations

scholarly journals Islands and stretched horizon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Yoshinori Matsuo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Total System ◽  
Island Rule ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Ads Spacetime ◽  
Hole Geometry

Abstract Recently it was proposed that the entanglement entropy of the Hawking radiation contains the information of a region including the interior of the event horizon, which is called “island.” In studies of the entanglement entropy of the Hawking radiation, the total system in the black hole geometry is separated into the Hawking radiation and black hole. In this paper, we study the entanglement entropy of the black hole in the asymptotically flat Schwarzschild spacetime. Consistency with the island rule for the Hawking radiation implies that the information of the black hole is located in a different region than the island. We found an instability of the island in the calculation of the entanglement entropy of the region outside a surface near the horizon. This implies that the region contains all the information of the total system and the information of the black hole is localized on the surface. Thus the surface would be interpreted as the stretched horizon. This structure also resembles black holes in the AdS spacetime with an auxiliary flat spacetime, where the information of the black hole is localized at the interface between the AdS spacetime and the flat spacetime.

scholarly journals Aspects of Hyperscaling Violating geometries at finite cutoff

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Salomeh Khoeini-Moghaddam ◽  
Farzad Omidi ◽  
Chandrima Paul
Keyword(s):  
Phase Transition ◽  
Cross Section ◽  
Entanglement Entropy ◽  
Zero Temperature ◽  
First Order ◽  
Holographic Entanglement Entropy ◽  
First Order Phase Transition ◽  
Ads Spacetime ◽  
Discontinuous Phase ◽  
First Order Phase

Abstract Recently, it was proposed that a $$ T\overline{T} $$ T T ¯ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥ $$ \frac{I}{2} $$ I 2 for all values of the cutoff.

Aspects of subregion holographic complexity

2019 ◽  
Vol 28 (15) ◽  
pp. 1930023 ◽  
Author(s):  
Davood Momeni ◽  
Nayereh Majd ◽  
Mudhahir Al Ajmi
Keyword(s):  
Review Paper ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Conformal Field ◽  
Cavalieri Principle ◽  
Holographic Superconductors ◽  
Holographic Entanglement Entropy ◽  
Ads Spacetime ◽  
General Deformation ◽  
Ads Geometry

This is a mini-review about the rapidly growing subject of dual holographic complexity (HC) for subsystems in conformal field theory (CFT) using a subregion volume enclosed by the entangled area in the dual bulk theory. This proposal is named as HC = volume. We use this proposal to compute the HC for different geometries in bulk theory. Because this HC quantity diverges as a result of the existence of the UV cutoff in the CFT, we proposed a suitable regularization scheme by subtracting the contribution of the background (pure) AdS spacetime from the deformation of the AdS geometry. Furthermore, the time-dependent geometries are investigated using the AdS/CFT proposal and hence, we proposed a time-dependent copy for HC in such nonstatic geometries. As an attempt to make a relation between HC and holographic entanglement entropy (HEE), inspired from the pure geometrical origins, we showed that HC and HEE which are duals to different volumes/areas in the bulk theory would be connected in a universal form for a general deformation AdS geometry (called holographic Cavalieri principle). As a pioneering idea we build a holographic model for [Formula: see text] critically in black holes via regularized HC as the dual thermodynamic volume. The second-order phase transitions in two-dimensional holographic superconductors is explained by using the regularized HC as an order parameter. All the results presented in this mini-review are collected from the list of published works of the first author of this paper. In several cases, we gave further explanation and clarification to make the ideas more understandable to the community. Other proposals for complexity like complexity as on shell action are not included in this review paper.

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.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

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