entanglement entropy of disconnected regions - Staff.city.ac.uk - City ...

The entropy of disconnected regions from twist fields
• Similarly to the previous case, the partition function of the n-sheeted Riemann surface
can be expressed in terms of a correlation function of twist fields. In this case it is a four
point function:
〈T (r 1 ) ˜T (r 2 )T (r 3 ) ˜T (r 4 )〉 L
(n)
∫
[ ∫
]
∝ [dϕ 1 · · · dϕ n ] R
2 exp − d 2 x L (n) [ϕ 1 , . . . , ϕ n ](x)
C 0,r R 2
= Z n = Tr A∪B (ρ n A∪B)
• From a computational point of view, it is much more challenging to compute a four-point
function than a two-point function, even in the two-particle approximation.
• Some limiting cases, such as r 1,2 ≪ r 3,4 can be analyzed more easily.