  We explicitly construct unique non-equilibrium steady state (NESS) of
Lindblad master equation characterized by a Gibbs ensemble $\rho_{\text{NESS}}
\propto e^{-\beta \tilde{H}}$, where the effective Hamiltonian $\tilde{H}$
consists only of $U(1)$ conserved charges of the original Hamiltonian.
Specifically, when the original Hamiltonian has multiple charges, it is
possible to couple them with bathes at different temperature respectively, but
still leads to an equilibrium state. To access the Gibbs NESS, the jump
operators need to be properly chosen to fulfill quantum detailed balance
condition (qDBC). These jump operators are ladder operators for $\tilde{H}$ and
jump process they generate form a vertex-weighted directed acyclic graph
(wDAG). By studying the XX model and Fredkin model, we showcase how the Gibbs
state emerges as the unique steady state.
