Instability of Universal Terms in the Entanglement Entropy

TL;DR

This paper investigates the non-uniqueness of universal terms in the entanglement entropy of Maxwell theory in 2+1 dimensions, revealing ambiguities due to algebraic and symmetry considerations, and proposes mutual information as a more stable measure.

Contribution

It demonstrates the instability of universal entanglement entropy terms in Maxwell theory caused by algebraic ambiguities and shows mutual information's stability as a better probe.

Findings

Universal entropy terms depend on algebra assignation details.

Haag duality is broken in the algebraic structure of the model.

Mutual information exhibits stable universal behavior, unlike entropy.

Abstract

The role of symmetries in what concerns entanglement entropy has been extensively explored in the last years and revealed a profound connection with the quantum field theory's algebraic structure. Recently, it was found that some universal contributions to the entanglement entropy and mutual information may be non uniquely defined in theories with generalized symmetries. Here, we study this issue in detail in the particular case of the entanglement entropy of the Maxwell theory in $(2+1)$ dimensions for rotationally symmetric regions. In this setup, the problem can be dimensionally reduced to a half-line. We find that the only difference between the reduced problem for the Maxwell field and the reduced scalar free field stems from the Fourier angular $n=0$ mode. This simplification allows us to check explicitly the many issues that characterize models with broken global symmetries. Namely, we manifestly show that the additive algebras break Haag duality, and single out the non-local operators which are responsible for the failure of this property. More interestingly, we present concrete lattice realizations that confirm that the logarithmic "universal" term of the Maxwell entanglement entropy for disks depends on the details of the algebra assignation. This ambiguity hinders the identification of possible topological contributions characteristic of models with generalized symmetries and tarnishes its universal character. We further calculate the Maxwell mutual information for two nearly complementary concentric disks. We obtain the expected universal contribution with a log-log dependence and check that, unlike entropy, this is stable. Accordingly, this supports mutual information as the appropriate probe to sense additivity-duality breaking and the consequent universal topological contributions.