On the M\"obius transformation in the entanglement entropy of fermionic chains
Mathematical Physics
2016-05-02 v2 Statistical Mechanics
High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.
Keywords
Cite
@article{arxiv.1511.02382,
title = {On the M\"obius transformation in the entanglement entropy of fermionic chains},
author = {F. Ares and J. G. Esteve and F. Falceto and A. R. de Queiroz},
journal= {arXiv preprint arXiv:1511.02382},
year = {2016}
}
Comments
29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos corrected