  We present a semi-analytical approach for studying quantum thermal energy
transport beyond the weak system-bath coupling regime. Our treatment, which
results in a renormalized, effective Hamiltonian model is based on the reaction
coordinate method. In our technique, applied to the nonequilibrium spin-boson
model, a collective coordinate is extracted from each environment and added
into the system to construct an enlarged system. After performing additional
Hamiltonian's truncation and transformation, we attain an effective two-level
system with renormalized parameters, which is weakly coupled to its
environments, thus can be simulated using a perturbative Markovian quantum
master equation approach. We compare the heat current characteristics in our
method to other techniques, and demonstrate that we properly capture strong
system-bath signatures such as the turnover behavior of the heat current as a
function of system-bath coupling strength. We further investigate the thermal
diode effect and demonstrate that strong couplings moderately improve the
rectification ratio relative to the weak coupling limit. The effective
Hamiltonian method that we developed here offers fundamental insight into the
strong coupling behavior, and is computationally economic. Applications of the
method towards studying quantum thermal machines are anticipated.
