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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Hence we have<br />
Short- and large-distance <strong>entanglement</strong> <strong>entropy</strong> revisited<br />
Z n = D n ε 2d n<br />
〈T (0) ˜T (r)〉 L<br />
(n) ,<br />
S A = − lim<br />
n→1<br />
d<br />
dn Z n<br />
where D n is a normalisation constant, and d n is the scaling dimension <strong>of</strong> T [Calabrese,<br />
Cardy 2004]:<br />
d n = c<br />
12<br />
(<br />
n − 1 )<br />
n<br />
• Short distance: 0 ≪ L ≪ ξ, logarithmic behavior<br />
〈T (0) ˜T (r)〉 L (n) ∼ r −2d n<br />
⇒ S A ∼ c 3 log ( r<br />
ε<br />
)<br />
• Large distance: 0 ≪ ξ ≪ L, saturation<br />
〈T (0) ˜T (r)〉 L (n) ∼ 〈T 〉 2 L (n) ⇒ S A ∼ − c 3 log(m 1ε) + U
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