J. Stat. Mech. (2021) 093101 arXiv:2010.16348 [cond-mat.stat-mech]
Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
Jiaju Zhanga,b and M. A. Rajabpourc
a Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China
b SISSA and INFN, Via Bonomea 265, 34136 Trieste, Italy
c Instituto de Fisica, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Gragoatá 24210-346, Niterói, RJ, Brazil
E-mail: jiajuzhang@tju.edu.cn, mohammadali.rajabpour@gmail.com
Abstract
We investigate the energy eigenstate Rényi 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 Rényi entropy takes a universal form, which is independent of the model, the quasiparticle momenta, and the subsystem connectedness. We calculate analytically the Rényi entropy in the extremely gapped limit and find different additional contributions to the universal Rényi entropy in various models. The corrections to the universal Rényi entropy cannot be neglected when the momentum differences of the excited quasiparticles are small. The Rényi 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 Rényi entropy written as the permanent of a certain matrix. We support all of our analytical results with numerical calculations.
