Entanglement entropy and M\"obius transformations for critical fermionic chains

TL;DR

This paper explores a novel symmetry of entanglement entropy under M"obius transformations in critical fermionic chains, extending previous work to non-invariant and gapless cases, supported by analytical and numerical evidence.

Contribution

It extends the understanding of M"obius symmetry in entanglement entropy to critical and symmetry-breaking fermionic chains, revealing new invariance properties.

Findings

M"obius symmetry holds in non-critical and symmetry-breaking cases.

The symmetry extends to critical (gapless) fermionic chains.

Analytical and numerical results support the extended symmetry.

Abstract

Entanglement entropy may display a striking new symmetry under M\"obius 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.