Reexamination of Finite-Lattice Extrapolation of Haldane Gaps

TL;DR

This paper introduces two new methods for accurately estimating the Haldane gaps in one-dimensional Heisenberg antiferromagnets with spins up to S=5, confirming the asymptotic behavior as S approaches infinity.

Contribution

The paper presents novel extrapolation techniques and provides the first finite-size gap data for S=2 to S=5, validating the asymptotic formula for large S.

Findings

Haldane gap for S=1 estimated as 0.4104789 ± 0.0000013

Finite-size gaps for S=2 to S=5 obtained for the first time

Extrapolation methods demonstrated to be effective

Abstract

We propose two methods of estimating a systematic error in extrapolation to the infinite-size limit in the study of measuring the Haldane gaps of the one-dimensional Heisenberg antiferromagnet with the integer spin up to S=5. The finite-size gaps obtained by numerical diagonalizations based on Lanczos algorithm are presented for sizes that have not previously been reported. The changes of boundary conditions are also examined. We successfully demonstrate that our methods of extrapolation work well. The Haldane gap for S=1 is stimated to be $0.4104789 \pm 0.0000013$. We successfully obtain the gaps up to S=5, which make us confirm the asymptotic formula of the Haldane gap in $S\to\infty$.