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We study nonequilibrium steady states (NESSs) in quantum spin-1/2 chains incontact with two heat baths at different temperatures. We consider theweak-coupling limit both for spin-spin coupling in the system and forsystem-bath coupling. This setting allows us to treat NESSs with a nonzerotemperature gradient analytically. We develop a perturbation theory for thisweak-coupling situation and show a simple condition for the existence ofnonzero temperature gradient. This condition is independent of theintegrability of the system.

Origin of Temperature Gradient in Nonequilibrium Steady States in Weakly Coupled Quantum Spin Systems