Abstract
The Haldane gap of the S=2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.
Highlights
It is well-known that the Haldane conjecture1, 2) for gapped one-dimensional Heisenberg antiferromagnets for integer S provides considerable contributions to our understanding of quantum spin systems
Let us observe the situation for S=2, for which there are experimental studies exploring materials as its candidates.6, 7) Since the Haldane gap for S=2 is smaller than that for S=1, even though various theoretical studies have attempted to improve the estimate, the precision remained low until Wang et al.8) concluded from their DMRG study that the gap is estimated as
Let us observe the situation of ND studies of the S=2 Haldane gap
Summary
It is well-known that the Haldane conjecture1, 2) for gapped one-dimensional Heisenberg antiferromagnets for integer S provides considerable contributions to our understanding of quantum spin systems. The Haldane gap is the largest for S=1; the density matrix renormalization group (DMRG),3) quantum Monte Carlo (QMC),4) and numericaldiagonalization (ND)5) calculations give estimates that agree with each other to a very precise number of digits: Δ/J ∼ 0.41048, where Δ and J denote the gap value and the strength of the interaction defined later, respectively. 5, a convergence-acceleration technique is applied to a sequence of finite-size gaps up to 16 sites under the TBC; the gap is concluded to be
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