Incremental expansions for Hubbard-Peierls systems

TL;DR

This paper introduces an incremental expansion method combined with exact diagonalization to accurately compute ground state energies and properties of Hubbard-Peierls chains, including dimerization and phonon dynamics.

Contribution

The paper presents a novel approach combining incremental expansion with exact diagonalization to study Hubbard-Peierls systems, achieving high accuracy for ground state energies and phase transition analysis.

Findings

Ground state energies of infinite chains computed with less than 0.3% error.

Identification of a critical electron-phonon coupling g_c=0.69.

Observation of a maximum in the dimerization order parameter at nonzero U for g<g_c.

Abstract

The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.