The Haldane Gap of the \(S=7\) Antiferromagnetic Chain

Abstract

We examine the \(S=7\) Heisenberg antiferromagnet in one dimension by numerical-diagonalization method. This system reveals nonzero energy gap above the unique ground state in its spin excitation, namely the Haldane gap; its amplitude is extremely small. We have carried out our numerical-diagonalization calculations based on the Lanczos algorithm applied to finite-size clusters up to 12 sites as highly parallelized computations. We successfully estimate the \(S=7\) Haldane gap directly from our data under the twisted boundary condition. We successfully confirm the agreement between the asymptotic behavior determined by the systems up to \(S=6\) and our present result that is presently estimated in the \(S=7\) case. Our results deepen our understanding concerning quantum spin systems and quantum magnets.