Optimal rectification in the ultrastrong coupling regime

We study the effect of ultrastrong coupling on the transport of heat. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the strong-coupling formalism is necessary for correctly describing heat flow in a wide range of parameters, including moderate to low couplings. We present a situation in which the strong-coupling formalism predicts optimal rectification whereas the phenomenological approach predicts no heat flow in any direction, for the same parameter values.