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 in [1]. 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 [2].

了解耦合到多个储层的一维量子系统的复杂特性对分析方法和模拟技术都提出了挑战。幸运的是，在封闭系统研究中广泛使用的基于密度矩阵重整化组的工具，最近也扩展到了开放系统的处理。我们提出了一种基于最先进的矩阵乘积状态 (MPS) 和张量网络方法的这种方法的实现，它可以为各种参数组合产生准确的结果。与大多数使用时间演化达到稳态的方法不同，我们专注于一种与时间无关的算法，并专注于用与标准密度矩阵重整化组 (DMRG) 算法完全相同的语言来重铸问题，. 因此，它可以很容易地导出到任何可用的 DMRG 平台。我们表明这种实现适用于研究一维系统中的热传输。作为案例研究，我们专注于 XXZ 量子自旋链，并通过将自旋电流和磁化曲线与分析结果进行比较来对我们的结果进行基准测试。然后，我们探索超出可以分析计算的范围。我们的代码可以在 github 上的[2]上免费获得。