Sublogarithmic behaviour of the entanglement entropy in fermionic chains
Statistical Mechanics
2019-11-27 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szeg\H{o} Theorem or the Fisher-Hartwig conjecture.
Cite
@article{arxiv.1902.07540,
title = {Sublogarithmic behaviour of the entanglement entropy in fermionic chains},
author = {Filiberto Ares and José G. Esteve and Fernando Falceto and Zoltán Zimborás},
journal= {arXiv preprint arXiv:1902.07540},
year = {2019}
}
Comments
30 pages, 4 figures, 1 table. Final version to appear in JSTAT. One new figure. Some comments and references added