  Understanding the intricate properties of one-dimensional quantum systems
coupled to multiple reservoirs poses a challenge to both analytical approaches
and simulation techniques. Fortunately, density matrix renormalization
group-based tools, which have been widely used in the study of closed systems,
have also been recently extended to the treatment of open systems. We present
an implementation of such method based on state-of-the-art matrix product state
(MPS) and tensor network methods, that produces accurate results for a variety
of combinations of parameters. Unlike most approaches, which use the
time-evolution to reach the steady-state, we focus on an algorithm that is
time-independent and focuses on recasting the problem in exactly the same
language as the standard Density Matrix Renormalization Group (DMRG) algorithm,
initially put forward by M. C. Ba\~nuls et al. in Phys. Rev. Lett. 114, 220601
(2015). Hence, it can be readily exported to any of the available DMRG
platforms. We show that this implementation is suited for studying thermal
transport in one-dimensional systems. As a case study, we focus on the XXZ
quantum spin chain and benchmark our results by comparing the spin current and
magnetization profiles with analytical results. We then explore beyond what can
be computed analytically. Our code is freely available on github at
https://www.github.com/heitorc7/oDMRG.
