Detailed Lanczos study of one- and two-hole band structure and finite-size effects in the t-J model

We present accurate numerical results for low-lying one- and two-hole states in the t-J model on a 4x4 lattice. We find six level crossings in the one-hole ground state for 0<t/J<∞; accurate t/J values of these crossings and the associated ground-state quantum numbers are given. A degeneracy of k=(0,0) S=1/2, and S=3/2 one-hole levels at t/J=1/2 is noted, which is consistent with a recent analytical result. For small t/J, the S=1/2 one-hole and S=0 two-hole bandwidths on the 4x4 lattice are Wh=[1.190 445 7(1)]t and Whh=[2.575(4)]t2/J, respectively. The origin of these qualitatively different behaviors is discussed, and a simple relation is found between the small-(t/J) one-hole bandwidth and a static-hole ground-state matrix element. The linear-t term in Wh is apparently a finite-lattice artifact. As a measure of finite-size effects we determined the rms hole-hole separation in the two-hole ground states; we find evidence of important finite-size effects for t/J approx-gt 1, for which the rms hole-hole separation is clearly constrained by the 4x4 lattice. Intermediate-(t/J) hole separations and binding energies for 0.3 approx-lt t/J approx-lt 1, however, scale approximately as powers of t/J, and can be used to give bulk-limit estimates for t/J=3. In particular, we estimate that the bulk-limit ground-state rms hole-hole separation at t/J=3 is ∼1.8a0, corresponding to 7 A in the high-temperature superconductors