Universal Rényi Entropy of Quasiparticle Excitations

Abstract: The R\'enyi entropies of quasiparticle excitations in the many-body gapped systems show a remarkable universal picture which can be understood partially by combination of a semiclassical argument with the quantum effect of (in)distinguishability. The universal R\'enyi entropies are independent of the model, the quasiparticle momenta, and the connectedness of the subsystem. In this letter we calculate exactly the single-interval and double-interval R\'enyi entropies of quasiparticle excitations in the many-body gapped fermions, bosons, and XY chains. We find additional contributions to the universal R\'enyi entropy in the excited states with quasiparticles of different momenta. The additional terms are different in the fermionic and bosonic chains, depend on the momentum differences of the quasiparticles, and are different for the single interval and the double interval. We derive the analytical R\'enyi entropy in the extremely gapped limit, matching perfectly the numerical results as long as either the intrinsic correlation length of the model or all the de Broglie wavelengths of the quasiparticles are small. When the momentum difference of any pair of distinct quasiparticles is small, the additional terms are non-negligible. On the contrary, when the difference of the momenta of each pair of distinct quasiparticles is large, the additional terms could be neglected. The universal single-interval R\'enyi entropy and its additional terms in the XY chain are the same as those in the fermionic chain, while the universal R\'enyi entropy of the double intervals and its additional terms are different, due to the fact that the local degrees of freedom of the XY chain are the Pauli matrices not the spinless fermions. We argue that the derived formulas have universal properties and can be applied for a wider range of models than those discussed here.