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 transition.

29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos corrected

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Cited by in corpus (8)

• Symmetry resolved entanglement in free fermionic systems
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
• Boundary effects on symmetry resolved entanglement
• Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains
• Entanglement entropy in the Long-Range Kitaev chain
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• Entanglement entropy and Möbius transformations for critical fermionic chains
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping