Finite-size corrections in critical symmetry-resolved entanglement

TL;DR

This paper investigates how finite-size effects influence symmetry-resolved entanglement entropies in critical 1d quantum systems, revealing that the decay of corrections depends on whether the symmetry group is discrete or continuous.

Contribution

It provides a detailed analysis of finite-size corrections to entropy equipartition, highlighting the role of the symmetry group's nature in these corrections.

Findings

Discrete symmetry corrections decay algebraically with system size.

U(1) symmetry corrections decay logarithmically with system size.

Correction prefactors are linked to twisted overlaps.

Abstract

In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.