Error analysis of the density-matrix renormalization group algorithm for a chain of harmonic oscillators

TL;DR

This paper analyzes the errors in the density-matrix renormalization group algorithm when applied to a harmonic oscillator chain, highlighting how system size and targeted states influence accuracy and proposing ways to improve efficiency.

Contribution

It provides a detailed error analysis of DMRG for harmonic oscillator chains and discusses how to optimize the algorithm for better accuracy and efficiency.

Findings

Errors depend on system size and energy level structure.

Optimized bases improve the accuracy of DMRG results.

Targeting more states affects the error magnitude.

Abstract

We investigate the application of the density-matrix renormalization group (DMRG) algorithm to a one-dimensional harmonic oscillator chain and compare the results with exact solutions, aiming to improve the algorithm efficiency. It has been demonstrated that the algorithm can give quite accurate results if the procedure is proper organized, for example, by using the optimized bases. The errors of calculated ground state energy and the energy gap between the ground state and the first excited state are analyzed, which are found to be critically dependent upon the size of the system or the energy level structure of the studied system and the number of states targeted during the DMRG procedure.