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

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.

arXiv comment32 pages, 12 figures, submtted to JSTAT

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• One-Dimensional Fermi liquids
• Excited states of linear polyenes
• Flow equation approach to the sine-Gordon model
• Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling
• Dynamical model of the dielectric screening of conjugated polymers
• Bosonization of dimerized Hubbard chains

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