On the Möbius transformation in the entanglement entropy of fermionic chains

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...

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Bibliographic Details
Published inJournal of statistical mechanics Vol. 2016; no. 4; pp. 43106 - 43130
Main Authors Ares, Filiberto, Esteve, José G, Falceto, Fernando, de Queiroz, Amilcar R
Format Journal Article
LanguageEnglish
Published IOP Publishing and SISSA 28.04.2016
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Summary: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.
Bibliography:JSTAT_035P_1215
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2016/04/043106