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SUMMARY:An area law for the entropy of low-energy states - Lluis Masanes (
 ICFO)
DTSTART:20101028T131500Z
DTEND:20101028T141500Z
UID:TALK27016@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:It is often observed in the ground state of spatially-extended
  quantum systems with local interactions that the entropy of a large regio
 n is proportional to its surface area. In some cases\, this area law is co
 rrected with a logarithmic factor. This contrasts with the fact that in al
 most all states of the Hilbert space\, the entropy of a region is proporti
 onal to its volume. In this talk it is shown that low-energy states have (
 at most) an area law with the logarithmic correction\, provided two condit
 ions hold: (i) the state has sufficient decay of correlations\, (ii) the n
 umber of eigenstates with vanishing energy-density is not exponential in t
 he volume. These two conditions are satisfied by many relevant systems. Th
 e central idea of the argument is that energy fluctuations inside a region
  can be observed by measuring the exterior and a superficial shell of the 
 region.\n
LOCATION:MR4\, Centre for Mathematical Sciences
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