On the Möbius transformation in the entanglement entropy of fermionic chains
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 Möbius 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 transitions.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 April 2016
 DOI:
 10.1088/17425468/2016/04/043106
 arXiv:
 arXiv:1511.02382
 Bibcode:
 2016JSMTE..04.3106A
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos corrected