Bath-assisted transport in a three-site spin chain: Global versus local approach

Within the standard weak-coupling limit, the reduced dynamics of open quantum spin chains with their two end spins coupled to two distinct heat baths at different temperatures are mainly derived using the so-called global and local approaches, in which, respectively, the spin self-interaction is and is not taken into account. In order to compare the differences between the two regimes, we concentrate on an open three-site XX spin chain, provide systematic techniques to address the global and local asymptotic states, and then compare the asymptotic spin-transport features by studying the spin flux through the middle site. Based on the analytical expressions of the stationary states in the two regimes, we find that the local approach misses important global effects emerging as spin sink and source terms that can only be due to nonnegligible interspin interactions. Moreover, we show that the local asympotic transport features cannot be recovered from the global ones by letting the interspin coupling vanish, thus pointing to the existence of different coupling ranges where only one approach is physically tenable and possibly a region where the two descriptions may coexist.