Holographic entanglement entropy: an overview

By T. Nishioka, S. Ryu, T. Takayanagi. 2009

983 citations recorded by the source corpus.

In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c0b81abddb2df268e132afa90f11b0a69f0d1fa8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Takayanagi
2. R. Myers
3. V. Hubeny
4. T. Nishioka
5. M. Rangamani
6. T. Faulkner
7. D. Harlow
8. J. Maldacena

In Nuclear and High Energy Physics

1. T. Takayanagi
2. R. Myers
3. V. Hubeny
4. M. Rangamani
5. T. Nishioka
6. D. Harlow
7. T. Faulkner
8. J. Maldacena

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. D. Harlow
4. T. Nishioka
5. V. Hubeny
6. M. Rangamani
7. T. Faulkner
8. Aron C. Wall

Citations in the corpus

• Holographic Quantum Matter (2016, background): “The recent discovery [579; 638; 639] and proof [500] of the Ryu-Takayangi formula for entanglement entropy in theories with holographic duals suggests that a more refined understanding of how the bulk reorganizes the QFT degrees of freedom is within reach.”
• Extremal surfaces as bulk probes in AdS/CFT (2012, background): “Similarly, the entanglement entropy [32],[33] associated to a given region A in the boundary is related to the area of a co-dimension 2 extremal(5) surface ending on ∂A.”
• Holographic evolution of the mutual information (2011, background): “For quantum field theories with a holographic dual, the prescription to compute SA in the boundary theory through a bulk computation has been conjectured in [6, 7] for static backgrounds and then generalized to stationary and time dependent geometries in [8] (see [9] for a review).”
• Measuring entanglement entropy in a quantum many-body system (2015, background): “Recently, it was realized that the concept of entanglement has broad impact in many areas of quantum many-body physics, ranging from condensed matter [10] to high energy field theory [11] and quantum gravity [12].”
• Holographic mutual information is monogamous (2011, background): “tant, and the minimum is over surfaces M Ain the bulk that are homologous to A(i.e. A[M A = @afor some bulk region a). The RT formula satises many checks but should be regarded as a conjecture. (See [3, 4] for reviews and discussions.) Classical and quantum corrections to the bulk theory are known t”
• Holographic Fermi surfaces and entanglement entropy (2011, background): “5) (4)Similar estimations have already been done in [19, 23].”
• A Holographic View on Physics out of Equilibrium (2010, background): “An excellent summary of the developments in understanding this holographic entanglement entropy can be found in [217].”
• Holographic calculations of Rényi entropy (2011, background): “10) the leading divergence in the Rényi entropies will have the form of the ‘area law’ expected to appear in the entanglement entropy [5, 6].”
• On volumes of subregions in holography and complexity (2016, background): “g [1–18]) is a measure of the quantum correlations of a quantum state, and is extremely useful in many quantum systems, ranging from condensed matter physics to black hole physics.”
• Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “But how? One approach to this question is the Ryu–Takanayagi conjecture [448, 449], which states that the entanglement entropy associated with a region R in a holographic QFT is given by the area of the minimal-area surface in the bulk which ends at the boundary of the region R.”
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT (2013, background): “The homology condition which is part of the RT prescription [14] is satisfied for these geodesics.”
• Entanglement Renyi entropies in holographic theories (2010, background): “A more complete review can be found in [19].”