Optical phonons for Peierls chains with long-range Coulomb interactions

TL;DR

This paper investigates how long-range Coulomb interactions influence optical phonons and lattice dimerization in Peierls chains, using DMRG calculations to extend the understanding of electron-phonon coupling effects.

Contribution

It introduces a combined model with Hubbard and long-range Coulomb interactions and analyzes their effects on phonon frequencies and dimerization in Peierls chains.

Findings

Hubbard interaction enhances dimerization and phonon frequencies.

Long-range Ohno interaction has negligible effect at moderate Coulomb parameters.

Numerical results agree with analytic solutions for the H"uckel model.

Abstract

We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (H\"uckel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the H\"uckel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zig-zag chains using the density-matrix renormalization group (DMRG) method. We check our numerical approach against analytic results for the H\"uckel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.