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• Another twist field ˜T is associated to the inverse symmetry σ −1 , and we have ∫ [ ∫ ] 〈T (0) ˜T (r)〉 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 (ρ n A) C 0,r : ϕ i+1 ( x ) T(0) T ~ ( r) ϕ i ( x)
Locality in QFT • A field O(x) is local in QFT if measurements associated to this field are quantum mechanically independent from measurements <strong>of</strong> the energy density (or Lagrangian density) at sp<strong>ac</strong>e-like distances. That is, equal-time commutation relations vanish: [O(x, t = 0), L (n) (x ′ , t = 0)] = 0 (x ≠ x ′ ) . • This means that: O( x) (n) L [ ϕ, 1 ϕ ,..., ϕ ] 2 n ( x’ ) = • Branch-point twist fields are local fields in the n-copy theory.
Page 1: Entanglement entropy in 1+1 dimensi
Page 4 and 5: How and why to measure (or quantify
Page 6 and 7: - The maximally entangled state |gs
Page 8 and 9: Short- and large-distance entanglem
Page 10 and 11: Partition functions on multi-sheete
Page 14 and 15: Hence we have Short- and large-dist
Page 16 and 17: The entropy of disconnected regions
Page 18 and 19: The entropy of disconnected regions
Page 20 and 21: Some simple limit cases • When r
Page 22 and 23: Non-extensivity • In recent years

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