DETAILED LANCZOS STUDY OF ONE-HOLE AND 2-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 4 x 4 lattice. We find six level crossings in the one-hole ground state for 0 < t/J < infinity; 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 4 x 4 lattice are W(h) = [1.190 445 7(1)]t and W(hh) = [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 W(h) 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 greater-than-or-similar-to 1, for which the rms hole-hole separation is clearly constrained by the 4 x 4 lattice. Intermediate-(t/J) hole separations and binding energies for 0.3 less-than-or-similar-to t/J less-than-or-similar-to 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 almost-equal-to 1.8a0, corresponding to 7 angstrom in the high-temperature superconductors. The similarity to the observed in-plane coherence length of xi(ab) almost-equal-to 14 angstrom supports the identification of t-J model hole pairs with the Cooper pairs of high-temperature superconductivity.