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

Understand

We investigate the effect of a non-uniform 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 $1 \leq j \leq N-1$, and the system size N.

• This deformation introduces a smooth boundary to systems with open boundary conditions.
• When $m \geq 2$, 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.