  In the presence of symmetry, entanglement measures of quantum many-body
states can be decomposed into contributions arising from distinct symmetry
sectors. Here we investigate the decomposability of negativity, a measure of
entanglement between two parts of a generally open system in a mixed state.
While the entanglement entropy of a subsystem within a closed system can be
resolved according to its total preserved charge, we find that negativity of
two subsystems may be decomposed into contributions associated with their
charge imbalance. We show that this charge-imbalance decomposition of the
negativity may be measured by employing existing techniques based on creation
and manipulation of many-body twin or triple states in cold atomic setups.
Next, using a geometrical construction in terms of an Aharonov-Bohm-like flux
inserted in a Riemann geometry, we compute this decomposed negativity in
critical one-dimensional systems described by conformal field theory. We show
that it shares the same distribution as the charge-imbalance between the two
subsystems. We numerically confirm our field theory results via an exact
calculations for non-interacting particles based on a double-gaussian
representation of the partially transposed density matrix.
