Entanglement and alpha entropies for a massive scalar field in two dimensions
Horacio Casini,Marina Huerta +1 more
TLDR
In this article, the authors present exact results on universal quantities derived from the local density matrix ρ, for a free massive Dirac field in two dimensions, which can be written exactly in terms of the solutions of non-linear differential equations of the Painleve V type.Abstract:
We present some exact results on universal quantities derived from the local density matrix ρ, for a free massive Dirac field in two dimensions. We first find trρn in a novel fashion, which involves the correlators of suitable operators in the sine–Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painleve V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.read more
Citations
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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.
Journal ArticleDOI
Aspects of Holographic Entanglement Entropy
Shinsei Ryu,Tadashi Takayanagi +1 more
TL;DR: In this paper, a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence, and the relation between the entropy and central charges in 4D conformal fields is examined.
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Entanglement entropy and conformal field theory
Pasquale Calabrese,John Cardy +1 more
TL;DR: 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.
Journal ArticleDOI
Entanglement entropy and conformal field theory
Pasquale Calabrese,John Cardy +1 more
TL;DR: In this article, a conformal field theory approach to entanglement entropy 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.
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.
References
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Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Book
Quantum Field Theory and Critical Phenomena
TL;DR: In this paper, a renormalization group analysis is proposed to model the scaling behavior of a field theory in the large N limit of the ferromagnetic order at low temperature.
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Entanglement entropy and quantum field theory
Pasquale Calabrese,John Cardy +1 more
TL;DR: In this article, a systematic study of entanglement entropy in relativistic quantum field theory is carried out, where the von Neumann entropy is defined as the reduced density matrix ρA of a subsystem A of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, and the results are verified for a free massive field theory.
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Holographic Derivation of Entanglement Entropy from the anti de Sitter Space/Conformal Field Theory Correspondence
Shinsei Ryu,Tadashi Takayanagi +1 more