Boundary effects in the density-matrix renormalization group calculation

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.

9 pages, 8 figures, to appear in PRB

References in corpus (7)

• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Dimerization induced by the RKKY interaction
• Exact ground state of the sine-square deformed XY spin chain
• Suppression of finite-size effects in one-dimensional correlated systems
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation
• The one-dimensional Kondo lattice model at quarter-filling

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