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 1jN-1, and system size N. This deformation introduces a smooth boundary to systems with open-boundary conditions. When m2, 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.