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

Abstract

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 $1\le j\le N-1$, and the system size N. This deformation introduces a smooth boundary to systems with open boundary conditions. When $m\ge 2$, 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.

7 pages, 12 figures

References in corpus (2)

• DMRG and periodic boundary conditions: a quantum information perspective
• Connecting distant ends of one-dimensional critical systems by a sine-square deformation

Cited by in corpus (1)

• Exact ground state of the sine-square deformed XY spin chain