Suppression of finite-size effects in one-dimensional correlated systems

We investigate the effect of a nonuniform deformation applied to one-dimensional (1D) quantum systems, where the local energy scale is proportional to g(j) = [sin(j pi/N)](m) determined by a positive integer m, site index 1 <= j <= N - 1, and system size N. This deformation introduces a smooth boundary to systems with open-boundary conditions. When m >= 2, the leading 1/N correction to the ground-state energy per bond e(0)((N)) vanishes and one is left with a 1/N-2 correction, the same as with periodic boundary conditions. In particular, when m = 2, the value of e(0)((N)) obtained from the deformed open-boundary system coincides with the uniform system with periodic boundary conditions. We confirm the fact numerically for correlated systems, such as the extended Hubbard model, in addition to 1D free-fermion models.