Application of the finite-cell-scaling method to the one-dimensional Hubbard model

The finite-cell-scaling method is applied to the one-dimensional Hubbard model. In the half-filled-band case and at zero temperature, the numerical results obtained for the ground-state energy differ from the exact solution by approximately 1%. For the range 1<U/t<5, where U is the Coulomb interaction and t is the transfer integral, the value of the normalized gap Δt agrees well with the exact result while it differs significantly for 0.2<U/t<0.9. For the latter range, we show that the gap varies as (U/t)1/2exp[(a+bU/t)^-1], where a and b are negative constants which depend on the size of the system, instead of (U/t)1/2exp(-2πtU) as in the exact solution.