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We study the excited state R\'enyi entropy and subsystem Schatten distance inthe two-dimensional free massless non-compact bosonic field theory, which is aconformal field theory. The discretization of the free non-compact bosonictheory gives the harmonic chain with local couplings. We consider the fieldtheory excited states that correspond to the harmonic chain states withexcitations of more than one quasiparticle, which we call multi-particlestates. This extends the previous work by the same authors to more generalexcited states. In the field theory we obtain the exact R\'enyi entropy andsubsystem Schatten distance for several low-lying states. We also obtain theshort interval expansion of the R\'enyi entropy and subsystem Schatten distancefor general excited states. In the locally coupled harmonic chain we calculatenumerically the excited state R\'enyi entropy and subsystem Schatten distanceusing the wave function method. We find excellent matches of the analyticalresults in the field theory and numerical results in the gapless limit of theharmonic chain. We also make some preliminary investigations of the R\'enyientropy and the subsystem Schatten distance in the extremely gapped limit ofthe harmonic chain.

Excited state R\'enyi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states