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

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

2010-12-07

arxiv.org/abs/1012.1472v2

Phys. Rev. A 83, 052118 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

7 pages, 12 figures

Scientific paper

10.1103/PhysRevA.83.052118

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. We confirm the fact numerically for correlated systems, such as the extended Hubbard model, in addition to 1D free-Fermion models.

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