  We study the excited state R\'enyi entropy and subsystem Schatten distance in
the two-dimensional free massless non-compact bosonic field theory, which is a
conformal field theory. The discretization of the free non-compact bosonic
theory gives the harmonic chain with local couplings. We consider the field
theory excited states that correspond to the harmonic chain states with
excitations of more than one quasiparticle, which we call multi-particle
states. This extends the previous work by the same authors to more general
excited states. In the field theory we obtain the exact R\'enyi entropy and
subsystem Schatten distance for several low-lying states. We also obtain the
short interval expansion of the R\'enyi entropy and subsystem Schatten distance
for general excited states. In the locally coupled harmonic chain we calculate
numerically the excited state R\'enyi entropy and subsystem Schatten distance
using the wave function method. We find excellent matches of the analytical
results in the field theory and numerical results in the gapless limit of the
harmonic chain. We also make some preliminary investigations of the R\'enyi
entropy and the subsystem Schatten distance in the extremely gapped limit of
the harmonic chain.
