One Dimensional Mimicking of Electronic Structure: The Case for Exponentials

TL;DR

This paper introduces an exponential interaction model for one-dimensional atoms and chains that accurately mimics three-dimensional behavior, significantly reducing computational time in density matrix renormalization group calculations.

Contribution

The authors develop an exponential interaction that simplifies computations and closely resembles screened Coulomb interactions, improving efficiency and accuracy in one-dimensional quantum systems.

Findings

Exponential interaction reduces computational time compared to soft-Coulomb.

Model closely mimics three-dimensional screened Coulomb interaction.

Results validated for hydrogen atom, uniform gas, and small molecules.

Abstract

An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential greatly diminishes the computational time needed for calculating highly accurate quantities with the density matrix renormalization group. This is due to the use of a small matrix product operator and to exponentially vanishing tails. Furthermore, its more rapid decay closely mimics the screened Coulomb interaction in three dimensions. Choosing parameters to best match earlier calculations, we report results for the one dimensional hydrogen atom, uniform gas, and small atoms and molecules both exactly and in the local density approximation.