A c-theorem for entanglement entropy
202 citations recorded by the source corpus.
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 are obstacles to the naive generalizations of the entropic c-theorem to higher dimensions.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/592e70388f19ef727f4d4fe3ca18ed8db05103f4
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Holographic entanglement entropy: an overview (2009, background): “The boundary of A, which is denoted by ∂A, divides the manifold N into two submanifolds A and B.”
- Holographic c-theorems in arbitrary dimensions (2010, methodology): “One obstacle to generalizing their analysis to higher dimensions was that it was unclear what geometry to specify in calculating the entanglement entropy [62].”
- Holographic entanglement entropy in Lovelock gravities (2011, background): “To apply the reasoning of [93-94] the full result, not just the logarithmic term, is required; mainly because away from the conformal fixed point the EE depends on two, rather than one length scale, i.”
- A covariant holographic entanglement entropy proposal (2007, methodology): “Moreover, an analogue of the Zamolodchikov’s c-theorem (called entropic c-theorem) has been shown in [7, 8 ] (see also [9]).”
- Comments on holographic entanglement entropy and RG flows (2012, methodology): “J H E P 0 4 ( 2 0 1 2 ) 1 2 2 analysis of [2, 3].”
- On the RG running of the entanglement entropy of a circle (2012, background): “Therefore the above inequality establishes an entropic form of the Zamolodchikov’s c-theorem [2, 16]: the central charge of the ultraviolet fixed point is always greater than the one of the infrared fixed point.”
- Bulk curves from boundary data in holography (2013, background): “taining gravity. The organization of this paper is as follows. In Sec. 2 we introduce the spherical-RindlerAdS space and discuss its eld theory dual, which is a nite time strip of the eld theory 2See [16] for how this observation relates strong subadditivity to the c-theorem in two dimensions. 2 liv”
- Remarks on the entanglement entropy for disconnected regions (2008, background): “This indicates that the condition C (l) ≤ 0 coincides with the entanglement entropy c-theorem for this particular case [1, 21].”
- Analyticity and the Unruh effect: a study of local modular flow (2024, unknown): “…structure of subregions in quantum field theory [10, 16, 17], to compute entanglement quantities explicitly in CFT [15], to prove entropic versions of renormalization monotonicity theorems [18–20], and even to constrain the complexity hierarchy of bulk reconstruction in holography [21].”