Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior

Abstract

The one-dimensional Heisenberg antiferromagnets of large-integer-$S$ spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for $S=5$ and $6$. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for $S=5$ and $6$ are estimated to be $0.000050\pm 0.000005$ and $0.0000030\pm 0.0000005$, respectively. The asymptotic formula of the Haldane gap for $S\to \infty$ is examined from the new estimates to determine the coefficient in the formula more precisely.

5 pages, 3 figures, 2 tables, to be published in J. Phys. Soc. Jpn

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• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Large-Scale Numerical-Diagonalization Study of the Shastry-Sutherland Model
• Numerical Study of S=1/2 Heisenberg Antiferromagnet on the Floret Pentagonal Lattice
• Spin excitation of the Heisenberg antiferromagnet with frustration: from the bounce-lattice antiferromagnet through the maple-leaf-lattice antiferromagnet to the exact-dimer system
• Numerical Diagonalization Study of the Phase Boundaries of the S=2 Heisenberg Antiferromagnet on the Orthogonal Dimer Lattice