Analysis of a density matrix renormalization group approach for transport in open quantum systems

TL;DR

This paper presents a time-independent density matrix renormalization group method for studying transport in open quantum systems, specifically applied to the XXZ spin chain, providing accurate results and benchmarking against analytical solutions.

Contribution

The authors develop a time-independent DMRG-based algorithm for open quantum systems, compatible with existing platforms, and demonstrate its effectiveness in thermal transport analysis.

Findings

Accurate simulation of thermal transport in 1D quantum systems.

Benchmarking results align with analytical solutions.

Code availability facilitates further research.

Abstract

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.