Abstract

We set up a systematic framework to calculate Renyi entropies and matrix elements of the reduced density matrix for arbitrary states (e.g. excited states) in 1+1d conformal field theories. Our approach involves novel CFT techniques including transformation of descendant fields under conformal mappings and evaluation of descendant n-point functions. As applications we calculate the second Renyi entropies of several individual excited states in the Ising, the free boson and the three-state Potts models both with periodic and open boundary conditions. We check the predictions against numerics coming from DMRG (preliminary) and demonstrate that in principle we can indeed characterize any excited state in quantum critical systems in our present framework. We also find that in a certain range of the relative subsystem size the second Renyi entropy for excited states shows a "quasi thermodynamic" behavior: it is extensive but obeys a nonlinear 1st law analog and only depends on the excitation energy. As a further application we show (preliminary) results for ground and excited state Renyi entropies in the massive Ising model using a truncated conformal space approach.