Abstract
Excited states with total spin 1 of a series of one-dimensional Heisenberg models are examined by a variational method. These models have short-range exchange interactions which decrease linearly with the distance between spins. Their ground states are exactly the same complete dimer states as those of the Majumdar-Ghosh model. Variational wave functions for the excited states are constructed by modifying the ground states. Excitation spectra and excitation gaps are obtained in analytic forms for the models with various interaction ranges. The excitation gap increases with increasing interaction range and saturates to a constant value.
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