A c-theorem for the entanglement entropy

Abstract

The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c-theorem for the entanglement entropy in 1+1 dimensions. We present a simple derivation of this theorem and compare the associated c-functions with the Zamolodchikov's ones for the case of free fields. We discuss the various difficulties which obstacle the naive generalizations of the entropic c-theorem to higher dimensions.

6 pages, 2 figures. Talk given at the conference IRGAC 2006: 2nd. Intern. Conf. on Quantum Theories and Renormalization Group in Gravity and Cosmology (Barcelona, jun. 2006). Reference added

References in corpus (19)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement in a simple quantum phase transition
• On Geometric Entropy
• A finite entanglement entropy and the c-theorem
• Fine-grained entanglement loss along renormalization group flows
• Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities
• Geometric entropy, area, and strong subadditivity
• A proof of the irreversibility of renormalization group flows in four dimensions
• The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem
• Anomalies, Unitarity and Quantum Irreversibility
• On the Trace Anomaly as a Measure of Degrees of Freedom
• Entanglement and majorization in (1+1)-dimensional quantum systems
• Exact Consequences of the Trace Anomaly in Four Dimensions
• Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group

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