A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains

Understand

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global `microcanonical' constraint, i.e.

• conserving the total magnetization.
• We will show that this system has an additional discrete symmetry which is particular to the Liouvillean description of the problem.
• Such symmetry reduces the dynamics even more than what would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states.