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We investigate how entanglement in the mixed state of a quantum field theorycan be described using the cross-computable norm or realignment (CCNR)criterion, employing a recently introduced negativity. We study its symmetryresolution for two disjoint intervals in the ground state of the massless Diracfermion field theory, extending previous results for the case of adjacentintervals. By applying the replica trick, this problem boils down to computethe charged moments of the realignment matrix. We show that, for two disjointintervals, they correspond to the partition function of the theory on a toruswith a non-contractible charged loop. This confers a great advantage comparedto the negativity based on the partial transposition, for which the Riemannsurfaces generated by the replica trick have higher genus. This result empowersus to carry out the replica limit, yielding analytic expressions for thesymmetry-resolved CCNR negativity. Furthermore, these expressions provide alsothe symmetry decomposition of other related quantities such as the operatorentanglement of the reduced density matrix or the reflected entropy.

Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory