Density Matrix Renormalization Group Study of One-Dimensional Acoustic Phonons

TL;DR

This paper demonstrates how the density matrix renormalization group (DMRG) method can effectively study one-dimensional acoustic phonons by using a local oscillator basis, achieving accurate results with limited computational resources.

Contribution

The paper introduces a DMRG approach with a local oscillator basis to handle long-range interactions in 1D acoustic phonons, improving computational efficiency and accuracy.

Findings

Excellent agreement with exact solutions for harmonic chains

Effective handling of long-range interactions with local oscillator basis

Potential applicability to more complex phononic systems

Abstract

We study the application of the density matrix renormalization group (DMRG) to systems with one-dimensional acoustic phonons. We show how the use of a local oscillator basis circumvents the difficulties with the long-range interactions generated in real space using the normal phonon basis. When applied to a harmonic atomic chain, we find excellent agreement with the exact solution even when using a modest number of oscillator and block states (a few times ten). We discuss the use of this algorithm in more complex cases and point out its value when other techniques are deficient.