Correlation effects on the oscillator strength of optical absorption: Sum rule for the one-dimensional Hubbard model.

TLDR: In this article, the optical sum rule related to the mean kinetic energy of band electrons was evaluated for the one-dimensional Hubbard Hamiltonian and the case of a half-filled band was treated exactly using the Bethe ansatz solution of Lieb and Wu.

Abstract: The optical sum rule which is related to the mean kinetic energy of band electrons is evaluated for the one-dimensional Hubbard Hamiltonian. The case of a half-filled band is treated exactly using the Bethe ansatz solution of Lieb and Wu. The kinetic energy decreases monotonically as a function of U and tends to zero like 1/U for U\ensuremath{\rightarrow}\ensuremath{\infty}. For other band fillings the Gutzwiller ansatz is used. Correlation effects increase quadratically with the density n of electrons (or holes) for n\ensuremath{\ll}1 and exhibit a maximum at n=1 (i.e., for the half-filled band).