A finite entanglement entropy and the c-theorem

By H. Casini, M. Huerta. 2004

435 citations recorded by the source corpus.

Abstract The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a mixed density matrix with nonzero entropy. This is usually called entanglement entropy, and it is known to be divergent in quantum field theory (QFT). However, it is possible to define a finite quantity F ( A , B ) for two given different subsets A and B which measures the degree of entanglement between their respective degrees of freedom. We show that the function F ( A , B ) is severely constrained by the Poincare symmetry and the mathematical properties of the entropy. In particular, for one component sets in two-dimensional conformal field theories its general form is completely determined. Moreover, it allows to prove an alternative entropic version of the c-theorem for ( 1 + 1 ) -dimensional QFT. We propose this well-defined quantity as the meaningfull entanglement entropy and comment on possible applications in QFT and the black hole evaporation problem.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a586a33444302568e87d0a8769410ae107967bc2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Takayanagi
2. R. Myers
3. V. Hubeny
4. M. Rangamani
5. T. Nishioka
6. T. Faulkner
7. M. Headrick
8. A. Singh

In Atomic and Molecular Physics, and Optics

1. T. Takayanagi
2. R. Myers
3. T. Nishioka
4. T. Faulkner
5. E. Tonni
6. V. Hubeny
7. Pasquale Calabrese
8. M. Rangamani

In Nuclear and High Energy Physics

1. T. Takayanagi
2. R. Myers
3. V. Hubeny
4. T. Nishioka
5. T. Faulkner
6. M. Rangamani
7. M. Headrick
8. Thomas Hartman

Citations in the corpus

• Gaining (mutual) information about quark/gluon discrimination (2014, neutral): “[17–20]).”
• Holographic local quenches and entanglement density (2013, background): “The strong subadditivity [33] (refer to [34] for its application to field theories and to [35] for its holographic proof) is given by the inequality SA1∪A2 + SA2∪A3 ≥ SA1∪A2∪A3 + SA2 .”
• On the RG running of the entanglement entropy of a circle (2012, methodology): “In this paper we extend the analysis of [2] to the case of circles in d = 2 spatial dimensions.”
• Aspects of Holographic Entanglement Entropy (2006, methodology): “This function C(x) is positive and is also a monotonically decreasing function [42] with respect to x as in the Zamolodchikov’s c-function [43].”
• Relative entropy and holography (2013, background): “Further, it has provided new insights on the structure of renormalization group flows [4, 5].”
• Holographic mutual information is monogamous (2011, methodology): “For a free massless fermion in two dimensions, the entanglement entropy of an arbitrary collection of intervals was computed in [14, 15], and the result implies I3(A : B : C) = 0 for any A,B,C.”
• Gravity and the crossed product (2021, background): “Another analogy is with the many problems, such as those studied in [23, 24], in which entanglement entropy differences in quantum field theory are better defined than entanglement entropies.”
• Entanglement entropy and conformal field theory (2009, result): “Another calculation in agreement with Z Rn,2 can be found in [77].”
• Entanglement entropy and quantum field theory (2004, background): “Huerta,A nite entanglem ent entropy and the c-theorem ,2004 Preprint hep-th/0405111.”
• AdS bubbles, entropy and closed string tachyons (2006, background): “This is a natural generalization of the entropic c-function defined in two dimension [49][48].”
• A refinement of entanglement entropy and the number of degrees of freedom (2012, background): “[68] H. Casini and M. Huerta, Phys.”