Stability of d-wave superconductivity in the t-J model

الأصل · EN

We use a recently developed technique, which allows to perform few Lanczos steps on a given wavefunction even for large system sizes, to investigate the t-J model in the physical parameter region and to check the stability of the BCS d-wave variational wavefunction. Our statistical Lanczos algorithm, which extends and improves the one Lanczos step, has been extensively tested on the small L=18 sites cluster where many Lanczos iterations can be performed exactly. In this case, at doping δ 10% the BCS wavefunction represents a very good initial state to achieve extremely accurate energies and correlation functions with few Lanczos iterations. For large sizes (L≤ 98) the behavior is similar: the low-energy d-wave order parameter Pd is weakly affected by a couple of Lanczos iterations in the low doping δ 10% region, whereas the energy is considerably lowered. As a further test of our calculation we have computed the variance of the Hamiltonian ΔEₚ=(< H² >-< H >²)/L² on the BCS wavefunction with p=0,1,2 Lanczos steps. For large p, when the Lanczos algorithm converges to the exact ground state, the variance vanishes exponentially with increasing p. The remarkable reduction of the variance, observed for p=1,2 Lanczos steps even for the largest lattice size considered, suggests a smooth and rapid convergence to the exact ground state. These results support the existence of off-diagonal long-range d-wave superconducting order in the two-dimensional t-J model.