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→∞. For other band fillings the Gutzwiller ansatz is used. Correlation effects increase quadratically with the density n of electrons (or holes) for n≪1 and exhibit a maximum at n=1 (i.e., for the half-filled band).

• Received 23 January 1986

DOI:https://doi.org/10.1103/PhysRevB.33.7247