Perturbation theory for optical excitations in the one-dimensional extended Peierls–Hubbardmodel

Abstract

For the one-dimensional, extended Peierls–Hubbard model we calculate analytically theground-state energy and the single-particle gap to second order in the Coulomb interactionfor a given lattice dimerization. The comparison with numerically exact data fromthe density-matrix renormalization group shows that the ground-state energy isquantitatively reliable for Coulomb parameters as large as the bandwidth. Thesingle-particle gap can almost triple from its bare Peierls value before substantialdeviations appear. For the calculation of the dominant optical excitations, wefollow two approaches. In Wannier theory, we perturb the Wannier excitonstates to second order. In two-step perturbation theory, similar in spirit to theGW-BSEapproach (where the Bethe–Salpeter equation is solved for quasi-particles which are calculated in theGW-approximation), we form excitons from dressed electron–hole excitations. We find theWannier 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 the bandwidth.For triplet excitons, second-order perturbation theory quickly fails completely.