Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Abstract

Abstract. The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.arXiv:1501.04311v1 [cond-mat.stat-mech]

Spin structures and entanglement of two disjoint intervals in conformal field theories

“…Performing the replica limit for these expressions in order to get the entanglement entropy S A or the mutual information is still an open problem (see [24] for numerical extrapolations).…”

“…For the models mentioned above, Trρ n A have been written also for a generic number of disjoint intervals [23]. Since performing the replica limit n → 1 of the Renyi entropies (2) for these analytic expressions is a very difficult task, in [24] numerical extrapolations of the CFT analytic expressions have been done by employing the method suggested in [25], finding excellent agreement with the corresponding lattice results.…”

“…In terms of these matrices, from (24) and (29) we have that the partial transpose of the reduced density matrix can be written as…”

“…Plugging these expressions into (24), one gets the partial transpose of the spin reduced density matrix in terms of the Majorana fermions. Both ρ…”

On shape dependence of holographic entanglement entropy in AdS4/CFT3

“…In these cases, one can construct combinations of entanglement entropies which are finite as ε → 0: the simplest case is the mutual information I A 1 ,A 2 ≡ S A 1 + S A 2 − S A 1 ∪A 2 when A = A 1 ∪ A 2 . For two dimensional CFTs, the mutual information or its generalizations to more than two intervals encode all the CFT data of the model [38][39][40][41][42][43][44][45][46]. Some results for the mutual information are also known in 2 + 1 dimensions from the quantum field theory point of view, where the analysis is more difficult because of the non local nature of ∂A [47][48][49][50][51][52].…”