Comment on "Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of- Equilibrium Systems"

TL;DR

This paper critiques a recent TdDMRG method for quantum many-body systems, highlighting artifacts in current oscillation results and proposing improvements by integrating non-equilibrium ground state evolution.

Contribution

It identifies artifacts in the existing TdDMRG approach and suggests a method to enhance its accuracy by including non-equilibrium ground state dynamics.

Findings

Current oscillations are artifacts of the original method.

Incorporating non-equilibrium ground state evolution improves accuracy.

The proposed modifications address the artifacts in out-of-equilibrium simulations.

Abstract

In a recent Letter [Phys. Rev. Lett. 88, 256403(2002), cond-mat/0109158] Cazalilla and Marston proposed a time-dependent density- matrix renormalization group (TdDMRG) algorithm for the accurate evaluation of out-of-equilibrium properties of quantum many-body systems. For a point contact junction between two Luttinger liquids, a current oscillation develops after initial transient in the insulating regime. Here we would like to point out that (a) the observed oscillation is an artifact of the method; (b) the TdDMRG can be significantly improved by incorporating the non-equilibrium evolution of the goundstate into the density matrix.