  We compare the time evolution of entanglement measures after local operator
excitation in the critical Ising model with predictions from conformal field
theory. For the spin operator and its descendants we find that Renyi entropies
of a block of spins increase by a constant that matches the logarithm of the
quantum dimension of the conformal family. However, for the energy operator we
find a small constant contribution that differs from the conformal field theory
answer equal to zero. We argue that the mismatch is caused by the subtleties in
the identification between the local operators in conformal field theory and
their lattice counterpart. Our results indicate that evolution of entanglement
measures in locally excited states not only constraints this identification,
but also can be used to extract non-trivial data about the conformal field
theory that governs the critical point. We generalize our analysis to the Ising
model away from the critical point, states with multiple local excitations, as
well as the evolution of the relative entropy after local operator excitation
and discuss universal features that emerge from numerics.
