Infinite Volume Extrapolations of Finite Cluster Calculations, ---How Correct are These?

TL;DR

This paper examines the accuracy of infinite volume extrapolations from finite cluster calculations across four different physical scenarios, highlighting potential inaccuracies in such methods.

Contribution

It analyzes four distinct cases to assess the reliability of extrapolating finite cluster data to infinite systems, revealing possible errors.

Findings

Extrapolations can lead to incorrect results in physical property predictions.

Different cases show varying degrees of extrapolation reliability.

Highlights the need for careful validation of extrapolation methods.

Abstract

Extrapolations of numerical data obtained from finite cluster calculations to the infinite volume limit can often give incorrect results. We discuss four separate cases: (a) the intensity of the lowest two-photon absorption in the infinite polyene, (b) bond alternation in the infinite polyene, (c) Cooper type pairing in the simple Hubbard model, and (d) pairing within the extended Hubbard model.