Finite-lattice extrapolations for a Haldane gap antiferromagnet

TL;DR

This paper uses exact diagonalization and extrapolation techniques to accurately estimate the Haldane gap and ground state energy in a finite S=1 Heisenberg chain, providing precise numerical results.

Contribution

It introduces a refined extrapolation method for finite-lattice data, achieving high-precision estimates of the Haldane gap and ground state energy.

Findings

Haldane gap G=0.41049(2)

Ground state energy per site e=-1.401485(2)

Correlation length xi=6.2

Abstract

We present results of exact diagonalizations of the isotropic antiferromagnetic S=1 Heisenberg chain by the Lanczos method, for finite rings of up to N=22 sites. The Haldane gap G(N) and the ground state energy per site e(N) converge, with increasing N, faster than a power law. By VBS and Shanks transformations, the extrapolated values are G=0.41049(2) and e=-1.401485(2). The spin-spin correlation function is well fit by exp(-r/xi)/sqrt(r) with xi=6.2.