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We construct the nonequilibrium steady state (NESS) density operator of thespin-1/2 XXZ chain with non-diagonal boundary magnetic fields coupled toboundary dissipators. The Markovian boundary dis- sipation is found with whichthe NESS density operator is expressed in terms of the product of the Laxoperators by relating the dissipation parameters to the boundary parameters ofthe spin chain. The NESS density operator can be expressed in terms of anon-Hermitian transfer operator (NHTO) which forms a commuting family ofquasilocal charges. The optimization of the Mazur bound for the hightemperature Drude weight is discussed by using the quasilocal charges and theconventional local charges constructed through the Bethe ansatz.

Construction of the steady state density matrix and quasilocal charges for the spin-1/2 XXZ chain with boundary magnetic fields