Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model

The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2${\mathit{k}}_{\mathit{F}}$x)${\mathit{x}}^{\mathrm{-}3/2}$ ${\ln }^{1/2}$(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.