2000/06/23 by Federico Becca, Becca, Federico, Luca Capriotti +3 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/0006353
Proceedings of Advanced Research Workshop on "Open Problems in Strongly Correlated Electron Systems", Bled
arxiv created 2000/06/23 · arxiv updated 2009/11/30
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.