Exact results for the optical absorption of strongly correlated electrons in a half-filled Peierls-distorted chain

F. Gebhard, K. Bott, M. Scheidler, P. Thomas, S. W. Koch

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

In this, the second of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain, we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U, we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of bandwidth W, separated by the Hubbard interaction U. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum-dependent but static ground-state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spin degenerate. This corresponds to the Hubbard model at temperatures large compared with the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice distortion δ and a nearest-neighbour interaction V. We find that the optical absorption for V = 0 is dominated by a peak at ω = U and broad but weak absorption bands for |ω - U| ≤ W. For an appreciable nearest-neighbour interaction V < W/2, almost all the spectral weight is transferred to Simpson's exciton band which is eventually Peierls split.

Original languageEnglish (US)
Pages (from-to)13-46
Number of pages34
JournalPhilosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
Volume75
Issue number1
DOIs
StatePublished - Jan 1997

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Physics and Astronomy(all)

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