Entanglement Entropy and Quantum Field Theory
Pasquale Calabrese,John Cardy +1 more
TLDR
In this article, a systematic study of entanglement entropy in relativistic quantum field theory was carried out, and it was shown that the von Neumann entropy of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, can be computed in terms of the reduced density matrix rho_A of a subsystem.Abstract:
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result S_A\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length \xi is large but finite, we show that S_A\sim{\cal A}(c/6)\log\xi, where \cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.read more
Citations
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A finite entanglement entropy and the c-theorem
Horacio Casini,M. Huerta +1 more
TL;DR: It is shown that the function F ( A, B ) is severely constrained by the Poincare symmetry and the mathematical properties of the entropy, which allows to prove an alternative entropic version of the c-theorem for ( 1 + 1 ) -dimensional QFT.
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Entanglement entropy in free quantum field theory
Horacio Casini,Marina Huerta +1 more
TL;DR: In this paper, the authors introduce the general methods to calculate the entanglement entropy for free fields, within the Euclidean and real time formalisms, and describe the particular examples which have been worked out explicitly in two, three and more dimensions.
Journal ArticleDOI
Universal terms for the entanglement entropy in 2+1 dimensions
Horacio Casini,Marina Huerta +1 more
TL;DR: In this paper, it was shown that the entanglement entropy and alpha entropies corresponding to spatial polygonal sets in 2 + 1 dimensions contain a term which scales logarithmically with the cutoff.
Journal ArticleDOI
Holographic Calculations of Renyi Entropy
TL;DR: In this article, the Renyi entropy of a general CFT in d dimensions with a spherical entangling surface, in terms of certain thermal partition functions, is calculated in various holographic models.
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Entanglement Entropy and Higher Spin Holography in AdS$_3$
Jan de Boer,Juan I. Jottar +1 more
TL;DR: In this paper, a functional constructed from Wilson lines in the bulk Chern-Simons theory was proposed to compute entanglement entropy in the W_N CFTs via holographic methods.
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