Multi-charged moments of two intervals in conformal field theory

TL;DR

This paper computes multi-charged moments and symmetry-resolved entanglement measures for two disjoint intervals in 1+1 dimensional conformal field theories with U(1) symmetry, using replica methods and numerical checks.

Contribution

It introduces a method to calculate multi-charged moments in CFTs with background fluxes, enabling symmetry resolution of entanglement in complex bipartitions.

Findings

Derived explicit formulas for multi-charged moments in CFTs.

Validated theoretical results with numerical simulations of lattice models.

Abstract

We study the multi-charged moments for two disjoint intervals in the ground state of two $1+1$ dimensional CFTs with central charge $c=1$ and global $U(1)$ symmetry: the massless Dirac field theory and the compact boson (Luttinger liquid). For this purpose, we compute the partition function on the higher genus Riemann surface arising from the replica method in the presence of background magnetic fluxes between the sheets of the surface. We consider the general situation in which the fluxes generate different twisted boundary conditions at each branch point. The obtained multi-charged moments allow us to derive the symmetry resolution of the R\'enyi entanglement entropies and the mutual information for non complementary bipartitions. We check our findings against exact numerical results for the tight-binding model, which is a lattice realisation of the massless Dirac theory.