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 gj=[sin(jπ/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 e0(N) vanishes and one is left with a 1/N2 correction, the same as with periodic boundary conditions. In particular, when m=2, the value of e0(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.