Comprehensive numerical and analytical study of two holes doped into the two-dimensional t-J model

We report on a detailed examination of numerical results and analytical cal culations devoted to a study of two holes doped into a two-dimensional, squ are lattice described by the t-J model. Our exact diagonalization numerical results represent the first solution of the exact ground state of two hole s in a 32-site lattice. Using this wave function, we have calculated severa l important correlation functions, notably the electron momentum distributi on function and the hole-hole spatial correlation function. Further, by stu dying similar quantities on smaller lattices, we have managed to perform a finite-size scaling analysis. We have augmented this work by endeavouring t o compare these results to the :predictions of analytical work for two hole s moving in an infinite lattice. This analysis relies on the canonical tran sformation approach formulated recently for the t-J model. From this compar ison we find excellent correspondence between our numerical data and our an alytical calculations, We believe that this agreement is an important step helping to justify the quasiparticle Hamiltonian, and, in particular, the q uasiparticle interactions that result from the canonical transformation app roach. Also, the analytical work allows us to critique the finite-size scal ing ansatzes used in our analysis of the numerical data. One important feat ure that we can infer from this successful comparison involves the role of higher harmonics in the two-particle, d-wave symmetry bound state-the conve ntional [cos(k(x))-cos(k(y))] term is only one of many important contributi ons to the d-wave symmetry pair wave function. [S0163-1829(98)04044-2].