Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0505193 · International Journal of Quantum Information

ENTANGLEMENT ENTROPY AND QUANTUM FIELD THEORY: A NON-TECHNICAL INTRODUCTION

Pasquale Calabrese, John Cardy

Published Jun 1, 2006• 251 citations
arXivHTMLPDF

Abstract

We give a pedagogical and non-technical introduction to the quantum field theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional conformal field theory.
DOI
10.1142/s021974990600192x

Related papers

Entanglement entropy and conformal field theory

Pasquale Calabrese, John Cardy

We review the conformal field theory approach to entanglement entropy. 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.

arXiv:0905.4013•Journal of Physics A Mathematical and Theoretical•Dec 2, 2009•1,688 citations

A Note on Entanglement Entropy and Conformal Field Theory

Dmitri V. Fursaev

It is pointed out that the entanglement entropy of quantum fields near the horizon of a two-dimensional black hole can be derived by means of the conformal field theory. This can be done in a way analogous to the computation of the entropy of BTZ black holes. The important feature of the considered case is that the degrees of freedom of the conformal theory are states localized in the physical space-time.

arXiv:hep-th/9811122•Nov 13, 1998•6 citations

Entanglement entropy in conformal field theory: new results for disconnected regions

Pasquale Calabrese

The study of the entanglement properties of the ground-state of extended quantum systems has propelled an intense research activity at the crossroads of different disciplines such as statistical mechanics, quantum information, and quantum field theory. Quantifying the entanglement allowed an elegant and more precise characterization of many extended quantum systems. I present the results for one-dimensional systems at a quantum critical point that are described by a conformal invariant field theory. In particular, I present some recent results on the entanglement of disconnected regions and I discuss how these investigations reveal important features of the underlying conformal field theory.

Journal of Statistical Mechanics Theory and Experiment•Sep 23, 2010•14 citations

QUANTUM INFORMATION, ENTANGLEMENT AND ENTROPY

Siddharth Sharma

In this review I had given an introduction to axiomatic Quantum Mechanics, Quantum Information and its measure entropy. Also, I had given an introduction to Entanglement and its measure as the minimum of relative quantum entropy of a density matrix of a Hilbert space with respect to all separable density matrices of the same Hilbert space. I also discussed geodesic in the space of density matrices, their orthogonality and Pythagorean theorem of density matrix.

•Dec 5, 2020•1 citation

Entanglement entropy and quantum field theory

Pasquale Calabrese, John Cardy

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 ρ A logρ A corresponding to the reduced density matrix ρ 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 of Holzhey et al when A is a finite interval of length 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 ξ is large but finite, we show that , where 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.

arXiv:hep-th/0405152•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2004•3,264 citations

ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

ARPAN BHATTACHARYYA, ANINDA SINHA

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados–Teitelboim–Zanelli (BTZ) black hole, the Gibbons–Hawking–York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

arXiv:1305.3448•International Journal of Modern Physics D•Oct 1, 2013•4 citations
The study of the entanglement properties of the ground-state of extended quantum systems has propelled an intense research activity at the crossroads of different disciplines such as statistical mechanics, quantum information, and quantum field theory. Quantifying the entanglement allowed an elegant and more precise characterization of many extended quantum systems. I present the results for one-dimensional systems at a quantum critical point that are described by a conformal invariant field theory. In particular, I present some recent results on the entanglement of disconnected regions and I discuss how these investigations reveal important features of the underlying conformal field theory.
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 ρ A logρ A corresponding to the reduced density matrix ρ 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 of Holzhey et al when A is a finite interval of length 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 ξ is large but finite, we show that , where 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.
Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados–Teitelboim–Zanelli (BTZ) black hole, the Gibbons–Hawking–York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.