Truncated Lanczos method: Application to hole-doped spin ladders

The truncated Lanczos method using a variational scheme based on Hilbert space reduction as well as a local basis change [Dagotto et al., Phys. Rev. B $58,$ 12 063 (1998)] is reexamined. The energy is extrapolated as a power-law function of the Hamiltonian variance. This systematic extrapolation procedure is tested quantitatively on the two-leg t-$J$ ladder doped with two holes. For this purpose, we have carried out calculations of the spin gap and of the pair dispersion up to size $2\times 15.$