Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

TL;DR

This paper analytically studies the charge fluctuations and symmetry-resolved entanglement in two coupled critical free theories with a conformal interface, providing exact predictions and numerical validation.

Contribution

It introduces a method to analyze symmetry-resolved entanglement in conformal theories with defects, linking geometry and correlation functions.

Findings

Analytical expressions for full counting statistics and symmetry-resolved Rènyi entropies.

Numerical results confirm the analytical predictions with perfect agreement.

Characterization of spectral properties of correlation functions across the interface.

Abstract

We consider the ground state of two species of one-dimensional critical free theories coupled together via a conformal interface. They have an internal $U(1)$ global symmetry and we investigate the quantum fluctuations of the charge across the impurity, giving analytical predictions for the full counting statistics, the charged moments of the reduced density matrix and the symmetry resolved R\'enyi entropies. Our approach is based on the relation between the geometry with the defect and the homogeneous one, and it provides a way to characterise the spectral properties of the correlation functions restricted to one of the two species. Our analytical predictions are tested numerically, finding a perfect agreement.