Exact Ground and Excited States of a T-j Ladder Doped with Two Holes

A two chain ladder model is considered described by the strong coupling t− t′−J −J ′ Hamiltonian. For the case of two holes moving in a background of antiferromagnetically interacting spins, exact, analytical results are derived for the ground state energy and low-lying excitation spectrum. The ground state is a bound state of two holes with total spin S=0. The charge excitation is gapless and the spin excitation has a gap. The corresponding wavefunctions are also exactly determined. The bound hole pair is found to have symmetry of the d-wave type. In the limit of strong rung coupling, the model maps onto an effective hard core boson model which exhibits dominant superconducting pairing correlations.