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University of Cambridge > Talks.cam > CQIF Seminar > An area law for the entropy of low-energy states

## An area law for the entropy of low-energy statesAdd to your list(s) Download to your calendar using vCal - Lluis Masanes (ICFO)
- Thursday 28 October 2010, 14:15-15:15
- MR4, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Ashley Montanaro. It is often observed in the ground state of spatially-extended quantum systems with local interactions 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. This talk is part of the CQIF Seminar series. ## This talk is included in these lists:- All CMS events
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