Entanglement of disjoint intervals in CFT and Riemann surfaces

In the context of two dimensional conformal field theories (CFT), we review some analytical results describing the entanglement of disjoint intervals. In particular, we consider the Renyi entropies and on the moments of the partial transpose, which provide respectively the entanglement entropy and the logarithmic negativity through some replica limits. These analytic expressions are obtained as the partition function of the CFT model on some particular singular higher genus Riemann surfaces constructed through the replica method. For simple models like the compactified free boson and the Ising model, explicit expressions in terms of Riemann theta functions are presented. Numerical calculations on different lattice models which support the analytic results are also discussed.Non UBCUnreviewedAuthor affiliation: SISSAResearche