Simulating Lindbladian evolution with non-Abelian symmetries: Ballistic front propagation in the SU(2) Hubbard model with a localized loss

We develop a non-Abelian time evolving block decimation (NA-TEBD) approach to study 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.