  We develop a non-Abelian time evolving block decimation (NA-TEBD) approach to
study of open systems governed by Lindbladian time evolution, while exploiting
an arbitrary number of abelian or non-abelian symmetries. We illustrate this
method in a one-dimensional fermionic $SU(2)$ Hubbard model on a semi-infinite
lattice with localized particle loss at one end. We observe a ballistic front
propagation with strongly renormalized front velocity, and a hydrodynamic
current density profile. For large loss rates, a suppression of the particle
current is observed, as a result of the quantum Zeno effect. Operator
entanglement is found to propagate faster than the depletion profile, preceding
the latter.
