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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Extensivity<br />
• A property <strong>of</strong> the <strong>entropy</strong> <strong>of</strong> <strong>disconnected</strong> <strong>regions</strong> that has been recently investigated is<br />
its extensivity.<br />
• Extensivity implies that the <strong>entropy</strong> <strong>of</strong> <strong>disconnected</strong> <strong>regions</strong> can be expressed in terms <strong>of</strong><br />
the individual entropies <strong>of</strong> connected domains<br />
S A∪B = S A + S B + S C + S D − 1 2 (S A∪C + S B∪C + S A∪D + S B∪D )<br />
• In our twist field picture it would imply a relationship <strong>of</strong> the type<br />
d<br />
dn 〈T (r 1) ˜T (r 2 )T (r 3 ) ˜T d<br />
[<br />
(r 4 )〉 ∼ lim 〈T (r 1 )<br />
n→1 dn<br />
˜T (r 2 )〉 + 〈T (r 3 ) ˜T (r 4 )〉<br />
+〈T (r 1 ) ˜T (r 4 )〉 + 〈T (r 2 ) ˜T (r 3 )〉 − 〈T (r 1 ) ˜T (r 3 )〉 − 〈T (r 2 ) ˜T<br />
]<br />
(r 4 )〉<br />
lim<br />
n→1