From local to nonlocal Fermi liquid in doped antiferromagnets
  The variation of single-particle spectral functions with doping is studied numerically within the t-J model. It is shown that corresponding self energies change from local ones at the intermediate doping to strongly nonlocal ones for a weakly doped antiferromagnet. The nonlocality shows up most clearly in the pseudogap emerging in the density of states, due to the onset of short-range antiferromagnetic correlations. 
P. Prelovsek, J. Jaklic and K. Bedell