Spherical Deformation for One-Dimensional Quantum Systems

System-size dependence of the ground-state energy EN is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as EN/N − limN → ∞EN/N, is of the order of 1/N2 when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the viewpoint of the spherical geometry.