Entanglement entropy and Möbius transformations for critical fermionic chains

Abstract

Entanglement entropy may display a striking new symmetry under Möbius transformations. This symmetry was analysed in our previous work for the case of a non-critical (gapped) free homogeneous fermionic chain invariant under parity and charge conjugation. In the present work we extend and analyse this new symmetry in several directions. First, we show that the above mentioned symmetry also holds when parity and charge conjugation invariance are broken. Second we extend this new symmetry to the case of critical (gapless) theories. Our results are further supported by numerical analysis. For some particular cases, analytical demonstrations show the validity of the extended symmetry. We finally discuss the intriguing parallelism of this new symmetry and space-time conformal transformations.

38 pages, 8 figures. Final version published in JSTAT. Typos corrected, references updated