Boundary effects in the density-matrix renormalization group calculation

TL;DR

This paper examines how boundary conditions in DMRG calculations influence the appearance of artificial symmetry-breaking and long-range order, emphasizing the importance of choosing appropriate boundaries for accurate results.

Contribution

It provides a comparative analysis of different boundary conditions in DMRG and highlights the impact of open boundaries on the reliability of long-range quantum fluctuation calculations.

Findings

Open boundary conditions often produce unreliable results due to boundary effects.

Periodic and sin^2-deformed boundaries reduce boundary effects and maintain homogeneity.

Boundary condition dependence must be considered alongside system size and accuracy in DMRG studies.

Abstract

We investigate the boundary effect of the density matrix renormalization group calculation (DMRG), which is an artifactual induction of symmetry-breaking pseudo-long-range order and takes place when the long-range quantum fluctuation cannot be properly included in the variational wave function due to numerical limitation. The open boundary condition often used in DMRG suffers from the boundary effect the most severely, which is directly reflected in the distinct spatial modulations of the local physical quantity. By contrast, the other boundary conditions such as the periodic one or the sin^2-deformed interaction [A. Gendiar, R. Krcmar, and T. Nishino, Prog. Theor. Phys. {\bf 122}, 953 (2009)] keep spatial homogeneity, and are relatively free from the boundary effect. By comparing the numerical results of those various boundary conditions, we show that the open boundary condition sometimes gives unreliable results even after the finite-size scaling. We conclude that the examination of the boundary condition dependence is required besides the usual treatment based on the system size or accuracy dependence in cases where the long-range quantum fluctuation is important.