Correlations in a two--chain Hubbard model
  Equal time spin--spin and pair field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half-filling, the antiferromagnetic and pair field correlations both decay exponentially with the pair field having a much shorter correlation length. This is consistent with a gapped spin-liquid ground state. Below half--filling, the antiferromagnetic correlations become incommensurate and the spin gap persists. The pair field correlations appear to follow a power law decay which is similar to their non-interacting U=0 behavior. 
R.M. Noack, S.R. White, and D.J. Scalapino