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

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