Boundary effects on symmetry resolved entanglement

TL;DR

This paper investigates how boundaries affect symmetry resolved entanglement entropies in one-dimensional quantum systems, deriving exact formulas and revealing boundary-induced algebraic corrections to entanglement scaling.

Contribution

It provides new exact formulas for symmetry resolved entropies in boundary systems and establishes a relation between Toeplitz+Hankel and block Toeplitz matrices.

Findings

Boundary effects cause algebraic corrections to entanglement scaling.

Derived exact formulas for charged and symmetry resolved entropies.

Established a relation between spectra of Toeplitz+Hankel and block Toeplitz matrices.

Abstract

We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.