An area law for the entropy of low-energy states

Seminar date and time: 
Tuesday, 6 April, 2010 - 12:30
Affiliation: 
ICFO
Author: 
Lluis Masanes
Location: 
IFAE seminar room

It is often observed in the ground state of spatially-extended quantum systems with local inter-actions that the entropy of a large region is proportional to its surface area. In some cases, this area law is corrected with a logarithmic factor. This contrasts with the fact that in almost all states of the Hilbert space, the entropy of a region is proportional 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 conditions hold: (i) the state has sufficient decay of correlations, (ii) the number of eigenstates with vanishing energy-density is not exponential in the volume. These two conditions are satisfied by many relevant systems. The 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.

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