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Entanglement entropy and conformal field theory
Pasquale Calabrese,John Cardy +1 more
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In this paper, a conformal field theory approach to entanglement entropy in 1+1 dimensions is presented, and the authors show how to apply these methods to the calculation of the entropy of a single interval and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals.Abstract:
We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.read more
Citations
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Colloquium: Many-body localization, thermalization, and entanglement
TL;DR: Theoretically, many-body localized (MBL) systems exhibit a new kind of robust integrability: an extensive set of quasilocal integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization as mentioned in this paper.
Journal ArticleDOI
Measuring entanglement entropy in a quantum many-body system
Rajibul Islam,Ruichao Ma,Philipp M. Preiss,M. Eric Tai,Alexander Lukin,Matthew Rispoli,Markus Greiner +6 more
TL;DR: Making use of the single-site-resolved control of ultracold bosonic atoms in optical lattices, two identical copies of a many-body state are prepared and interfered to directly measure quantum purity, Rényi entanglement entropy, and mutual information.
Journal ArticleDOI
Holographic Entanglement Entropy: An Overview
TL;DR: In this article, the authors review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence.
Journal ArticleDOI
Entanglement Renyi entropies in holographic theories
TL;DR: The RT formula predicts a phase transition in the entanglement entropy as a function of their separation, and that the mutual information between the intervals vanishes for separations larger than the phase transition point.
Journal ArticleDOI
Time Evolution of Entanglement Entropy from Black Hole Interiors
Thomas Hartman,Juan Maldacena +1 more
TL;DR: In this paper, the authors compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states, and match the bulk and boundary computations of the entropy in the case of a two-dimensional CFT.
References
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Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Journal ArticleDOI
Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory
TL;DR: In this paper, the authors present an investigation of the massless, two-dimentional, interacting field theories and their invariance under an infinite-dimensional group of conformal transformations.
Journal ArticleDOI
Holographic Derivation of Entanglement Entropy from the anti de Sitter Space/Conformal Field Theory Correspondence
Shinsei Ryu,Tadashi Takayanagi +1 more
TL;DR: It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.
Book
Conformal Field Theory
TL;DR: This paper developed conformal field theory from first principles and provided a self-contained, pedagogical, and exhaustive treatment, including a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algesas.
Journal ArticleDOI
Entanglement in many-body systems
TL;DR: In this article, the properties of entanglement in many-body systems are reviewed and both bipartite and multipartite entanglements are considered, and the zero and finite temperature properties of entangled states in interacting spin, fermion and boson model systems are discussed.
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