Quasi-Particles in the Strong-Coupling Limit of the 2D Hubbard Model

The single-particle Green's function for the strong-coupling limit of the single-band Hubbard model ( t-J model) at half-filling is calculated numerically using a Lanczos algorithm. Two-dimensional systems of up to 18 sites with periodic boundary conditions are examined, and evidence is presented for a coherent quasi-particle band of width J which emerges at the low-energy edge of the incoherent spectrum. We find the quasi-particle dispersion to be consistent with ε k = ( J /2)[cos ( k x ) + cos ( k y )] 2 , corresponding to effective next-nearest-neighbour hopping.