Corrections to universal R\'enyi entropy in quasiparticle excited states of quantum chains

We investigate the energy eigenstate R\'enyi entropy of generic bipartition in the fermionic, bosonic, and spin-1/2 XY chains. When the gap of the theory is large or all the momenta of the excited quasiparticles are large, the R\'enyi entropy takes a universal form, which is independent of the model, the quasiparticle momenta, and the subsystem connectedness. We calculate analytically the R\'enyi entropy in the extremely gapped limit and find different additional contributions to the universal R\'enyi entropy in various models. The corrections to the universal R\'enyi entropy cannot be neglected when the momentum differences of the excited quasiparticles are small. The R\'enyi entropy derived in the extremely gapped limit is still valid in the slightly gapped and even critical chains as long as all the momenta of the excited quasiparticles are large. In the case of double interval in the XY chain we find new universal results and their corrections. We call the result universal even though it is only valid for double interval in the spin-1/2 XY chain. In the case of the bosonic chain in the extremely massive limit we find analytically a novel formula for the R\'enyi entropy written as the permanent of a certain matrix. We support all of our analytical results with numerical calculations.