Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model

TL;DR

This paper analytically investigates optical excitations in the one-dimensional extended Peierls--Hubbard model, comparing perturbation approaches with numerical data, and finds Wannier theory more reliable than two-step perturbation for certain parameters.

Contribution

It introduces second-order perturbation methods for calculating optical excitations in the extended Peierls--Hubbard model and compares their effectiveness.

Findings

Ground-state energy is reliable up to large Coulomb interactions.

Single-particle gap can nearly triple before deviations occur.

Wannier theory outperforms two-step perturbation for exciton calculations.

Abstract

For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.