Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

TL;DR

This paper demonstrates that the density matrix renormalization group (DMRG) method can effectively analyze non-equilibrium systems, specifically the asymmetric exclusion process, providing accurate results with minimal computational resources.

Contribution

The study applies DMRG to a non-equilibrium problem and shows it achieves high accuracy in calculating stationary states with fewer bases than traditional methods.

Findings

DMRG accurately reproduces the exact particle density profile.

Small basis sets in DMRG yield results in excellent agreement with exact solutions.

The approach offers an efficient alternative for non-equilibrium statistical mechanics problems.

Abstract

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.