Remarks on the entanglement entropy for disconnected regions

Details Remarks on the entanglement entropy for disconnected regions Remarks on the entanglement entropy for disconnected regions

2008-12-09

arxiv.org/abs/0812.1773v2

JHEP 0903:048,2009

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 4 figures, some additions

Scientific paper

10.1088/1126-6708/2009/03/048

Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures.

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