On the Möbius transformation in the entanglement entropy of fermionic chains

Filiberto Ares, José G Esteve, Fernando Falceto, Amilcar R de Queiroz
2016 Journal of Statistical Mechanics: Theory and Experiment  
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
more » ... s give further support for the use of entanglement entropy to analyse phase transition.
doi:10.1088/1742-5468/2016/04/043106 fatcat:2qwsvy3znbd2xmb37gxxtf7tce