entanglement entropy of disconnected regions - Staff.city.ac.uk - City ...
entanglement entropy of disconnected regions - Staff.city.ac.uk - City ...
entanglement entropy of disconnected regions - Staff.city.ac.uk - City ...
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• When r 1 ≪ r 2 and r 3 ≪ r 4 the 4-point function f<strong>ac</strong>torizes as<br />
d<br />
lim<br />
n→1 dn 〈T (r 1) ˜T (r 2 )T (r 3 ) ˜T d<br />
(r 4 )〉 → lim<br />
n→1 dn 〈T (r 1)〉〈 ˜T (r 2 )T (r 3 )〉〈 ˜T (r 4 )〉<br />
= lim 〈T 〉 2 d<br />
n→1 dn 〈 ˜T (r 2 )T (r 3 )〉 + lim 〈 ˜T (r 2 )T (r 3 )〉 d 〈T 〉2<br />
n→1 dn<br />
d〈T 〉<br />
= −S C + 2 lim<br />
n→1 dn<br />
• In this case the size <strong>of</strong> <strong>regions</strong> A and B tends to ∞ while the size <strong>of</strong> region C is fixed<br />
and finite. Region C only sees the infinite <strong>regions</strong> A and B and its <strong>entanglement</strong> with<br />
them is S C . To this we add the two “boundary” contributions from the <strong>entanglement</strong> <strong>of</strong> A<br />
and B with D.<br />
• These two examples are compatible with extensivity <strong>of</strong> the <strong>entanglement</strong> <strong>entropy</strong>!
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