HALDANE-GAP IN THE S=1 HALDANE-SHASTRY MODEL

We present evidence that the S = 1 Haldane-Shastry model has a gap in the energy spectrum, extending to the case of a model with long-range interactions results previously obtained by Haldane and, numerically, by other authors for the case of short-range interactions. We studied the groundstate and first excited state using a modified Lanczos algor ithm and obtained the low temperature behavior diagonalizing exactly s mall chains. The correlation functions decay exponentially with distan ce and the low-T susceptibility decays exponentially to zero. The gap is larger than for the Heisenberg model and the correlation functions decay faster indicating a smaller correlation length.