Abstract
Using the technique of exact diagonalization, the whole spectrum of the Hamitonian of the t-J model with one hole in clusters of 8 and 16 sites were obtained. Using group theory, translational and reflection symmetries in real space as well as spin inversion symmetry in spin space could be applied to reduce our matrix size. The static magnetic susceptibility, the dynamic spin-spin correlation and the spin-charge correlation of the above systems as a function of temperature were reported. A comparison between the result obtained by finite temperature Lanczos diagonalization (FTLD) and ours was made.