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Bulletin of the American Physical Society

Ground State of the One Dimensional Heisenberg Model with {\it NNN} Interactions

Jay D. Mancini, Vassilios Fessatidis, S.P. Bowen, J Malý, Robert K. Murawski

Published Mar 17, 2016• 0 citations
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arXiv:cond-mat/9508124•Journal of Applied Physics•Apr 15, 1996•2 citations
Ground-state properties are studied for the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions. The energy, the singlet-triplet energy gap, the two-spin correlation function, and the den Nijs and Rommelse string correlation function in the ground states of finite-size systems of up to 16 spins are calculated exactly. By extrapolating these results, the ground-state properties at the infinite-size limit are discussed. It is found, in particular, that as the ratio of the nnn interaction constant to the nn one increases, the string order parameter (the limiting value of the longest-distance string correlation function) as well as the Haldane gap (the limiting value of the singlet-triplet energy gap) divided by the sum of both interaction constants increases. This result implies that the competition between the antiferromagnetic nn and nnn interactions stabilizes the Haldane phase.
For special coupling ratios, the one-dimensional (1D) s=1/2 Heisenberg model with antiferromagnetic nearest and next-nearest neighbor interactions has a pure dimer ground state, and the 1D s=1 Heisenberg model with antiferromagnetic bilinear and biquadratic interactions has an exact valence-bond-solid ground state. The recursion method is used to calculate the T=0 spin dynamic structure factor for both models and, for the s=1/2 model, also the dimer dynamic structure factor. New results for line shapes and dynamically relevant dispersions are obtained.