Holographic entanglement entropy and emergent spacetime. Entanglement entropy from a holographic viewpoint nasaads. Holographic derivation of entanglement entropy from the antide sitter space conformal field theory. In any cft with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to cft states. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the wheelerdewitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three.
The discovery of adscft correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important. We compute entanglement entropy in a variety of holographic systems, paying particular attention to its longdistance behaviour, characterised by a term proportional to surface area. Abstract arxiv the entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The general lessons one can learn from this connection are drawn. This includes setting up a scheme in which we can compute the relative entropy. In the second part, an overview of the adscft correspondence is given and the holographic entanglement entropy prescription is explained. Black hole entropy includes and may be 100% vacuum entanglement it seems natural that gravity would cut off the entanglement of pairs separated by less than the planck length, since they would be engulfed in a virtual black hole.
In the third part, the timedependence of entanglement entropy in outofequilibrium systems, and applications to many body physics are explored using holographic methods. Holographic entanglement entropyfrom adscft here we. Entanglement entropy obeys a first law, an exact quantum generalization of the ordinary first law of thermodynamics. We present a natural generalization of holographic entanglement entropy proposals beyond the scope of ads cft by anchoring extremal surfaces to holographic screens. Holographic entanglement entropy mukund rangamani springer. After that we will explain the holographic entanglement entropy with a brief introduction to the adscft correspondence. We study holographic entanglement entropy in fourdimensional quantum gravity with negative cosmological constant. Holographic entanglement entropy mukund rangamani, tadashi takayanagi auth. Field theory holographic dual entanglement entropy is given by the area of a minimal surface codimension2 whose boundary is fixed to be the entangling surface newtons constant area of minimal surface ryu, takayangi hepth0603001 inspired by bekensteinhawking entropy.
Various aspects of holographic entanglement entropy and mutual information theoretical physics masters thesis april 2014 100 holography, entanglement entropy, mutual information kumpula campus library entanglement entropy is a proposal to quantify quantum entanglement of. Entanglement entropy from a holographic viewpoint iopscience. The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the. In this paper we introduce holographic diagrammatic software for quantum information, and we illustrate its use. This is simply summarized into the formula s a area. Liu discusses how to calculate the entanglement entropy of a boundary system using the ads gravity. Holographic entanglement entropy lecture notes in physics. The two entanglement entropies agree up to an additional term, the origin of which may be attributed to the conformal anomaly of even dimensional defects as we discuss. Holographic software for quantum networks arthur ja e.
A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. We use the term \ holographic, since one can trans. For time dependent case, additional assumptions are necessary. Entanglement growth during thermalization in holographic. However, in the context of gaugegravity duality, holographic entanglement entropy was proposed by ryu and takayanagi rt to be captured by the area of a. Holographic screens are a natural extension of the ads boundary to arbitrary spacetimes and are preferred codimension1 surfaces from the viewpoint of the covariant entropy bound. Title entanglement entropy from a holographic viewpoint issue date url this is an authorcreated, uncopyedited version of an article accepted for publication in classical and quantum gravity. Proved by lewkowyczmaldacena is the minimal area surface codim. In a thermalization of cft, an initially pure state gets excited and evolves until it reaches a thermal equilibrium. However, the entanglement entropy of such a cft follows the calabresecardy formula or the ryu.
If there is a stationary black hole in the bulk, then the holographic entropy is related to the black hole entropy. We then provide a holographic derivation of the conjecture which highlights someofthesubtletiesinvolved. Lectures on entanglement entropy in field theory and holography. We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. Quantum holographic entanglement entropy to all orders in. With an aim towards understanding the timedependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hepth0603001. The quenches are such that a spatially uniform density of energy is injected at an instant in time, exciting a strongly coupled conformal field theory which eventually equilibrates.
Entanglement of purification through holographic duality. We argue that the degrees of freedom in a ddimensional cft can be reorganized in an insightful way by studying observables on the moduli space of causal. Within the context of the adscft correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The entanglement entropy is a good probe to quantum phase transitions and various phases in quantum field theory and manybody system. He gives a holographic proof of the strong subadditivity conditions of the entanglement entropy, and discusses a simple example. Bit threads and holographic entanglement of purification.
The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. We start by introducing the concept of entanglement entropy in chapter 2. The holographic entanglement and free energy is computed for fivedimensional super conformal field theories, starting from their holographic supergravity duals. The discovery of adscft correspondence leads to the idea of holographic entanglement entropy, which is a. This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. The discovery of adscft correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. Holographic entanglement entropy lecture notes in physics book 931 kindle edition by rangamani, mukund, takayanagi, tadashi, takayanagi, tadashi. Holographic fermi surfaces and entanglement entropy. Use features like bookmarks, note taking and highlighting while reading holographic entanglement entropy lecture notes in physics book 931.
Holographic entanglement entropy in 2d holographic. Holographic entanglement entropy refers to the expression of entanglement entropy of quantum field theories expressed holographically via a version of adscft duality in terms of the geometry of a higherdimensional bulk spacetime. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. Holographic entanglement entropy conjecture for general. In this way, a relation between holographic geometry and entanglement entropy was established. Entanglement entropy from a holographic viewpoint inspire. The discovery of antide sitterconformal field theory correspondence has led to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity.
Download it once and read it on your kindle device, pc, phones or tablets. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Title entanglement entropy from a holographic viewpoint. The aim of the present letter is to find the holographic entanglement entropy hee in 2d holographic superconductors hsc. A 4g n, 2 where s a is the entanglement entropy for the subsystem a, and. The discovery of antide sitter conformal field theory correspondence has led to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. This is called the holographic entanglement entropy. We will discuss the holographic interpretation of the. A is a codimension two minimal area surface whose boundary a coincides with. Holographic entanglement entropy and second law of black. Indeed, it is possible to compute the exact form of this entropy due to an advantage of approximate solutions inside normal and superconducting phases with backreactions. Holographic entanglement entropy in the presence of defects.
Holographic entanglement entropy for interface, defect or. It contains almost anything youd want to know about entanglement and references to the rest. According to it, the holographic entanglement entropy associated to a boundary region is given by the maximum flux of a bounded, divergenceless vector field, through the corresponding region. A covariant holographic entanglement entropy proposal. Moreover, the holographic entanglement entropy allows us to answer the basic puzzle on the entropy of timedependent back holes 117, 119. The time evolution of holographic entanglement entropy under local quenches has been studied in. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. Indeed, in twodimensional conformal field theory, the entanglement entropy is proportional to the central charge in twodimensional conformal field theories 2d cfts as shown in 20, 21, where a general prescription of computing the entropy in 2d cfts is given. In chapter 3 we consider the entanglement of a cft.
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