DMRG studies on linear-exchange quantum spin models in one dimension
arXiv:1207.0636 · doi:10.1209/0295-5075/100/27003
Abstract
We study a class of spin-1/2 quantum antiferromagnetic chains using DMRG technique. The exchange interaction in these models decreases linearly as a function of the separation between the spins, for . For the separations beyond , the interaction is zero. The range parameter takes positive integer values. The models corresponding to all the odd values of are known to have the same exact doubly degenerate dimer ground state as for the Majumdar-Ghosh (MG) model. In fact, R=3 is the MG model. For even , the exact ground state is not known in general, except for R=2 (the Bethe ansatz solvable Heisenberg chain) and in the asymptotic limit of where the two MG dimer states again emerge as the exact ground state. In the present work, we numerically investigate the even- models whose ground state is not known analytically. In particular, for R=4, 6 and 8, we have computed a number of ground state properties. We find that, unlike R=2, the higher even- models are spin-gapped, and show strong dimer-dimer correlations of the MG type. Moreover, the spin-spin correlations decay very rapidly, albeit showing weak periodic revivals.
arXiv comment8 pages, 12 figures
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