  We study the thermalization properties of one-dimensional open quantum
systems coupled to baths at their boundary. The baths are driven to their
thermal states via Lindblad operators, while the system undergoes Hamiltonian
dynamics. We specifically consider multi-site baths and investigate the extent
to which the late-time steady state resembles a Gibbs state at some
controllable temperature set by the baths. We study three models: a
non-interacting fermion model accessible via free-fermion technology, and two
interacting models, the XZ model and the chiral clock model, which are
accessible via tensor network methods. We show that, by tuning towards the weak
coupling and slow relaxation limits, one can engineer low temperatures in the
bulk of the system provided the bath size is big enough. We use this capability
to study energy transport in the XZ model at lower temperatures than previously
reported. Our work paves the way for future studies of interacting open quantum
systems at low temperatures.
