Low-energy states with different symmetries in the t-J model with two holes on a 32-site lattice

We study the low-energy states of the t-J model with two holes on a 32-site lattice with periodic boundary conditions. In contrary to common belief, we find that the state with d_x2-y2 symmetry is not always the ground state in the realistic parameter range 0.2≤J/t≤0.4. There exist low-lying finite-momentum p states whose energies are lower than the d_x2-y2 state when J/t is small enough. We compare various properties of these low-energy states at J/t=0.3 where they are almost degenerate and find that those properties associated with the holes (such as the hole-hole correlation and the electron momentum distribution function) are very different between the d_x2-y2 and p states, while their spin properties are very similar. Finally, we demonstrate that by adding "realistic" terms to the t-J model Hamiltonian, we can easily destroy the d_x2-y2 ground state. This casts doubt on the robustness of the d_x2-y2 state as the ground state in a microscopic model for the high-temperature superconductors.