2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27610We present an exact diagonalization study of the low energy singlet and triplet states for both 1D and 2D t-J model. A scan of the parameter ratio J/t shows that for nearly all low energy states in both 1D and 2D the excitation energy takes the linear form E(t,J) = a t + b J. In 1D this is the natural consequence of the factorization of the low energy wave functions, i.e. spin-charge separation. Examination of the low energy eigenstates in 2D shows that in the singlet sector the lowest states are collective modes, which for larger J correspond to `dynamical hole columns', i.e. a periodic modulation of the hole density. This modulation is well reproduced by treating holes as hard-core Bosons with an attractive interaction.Revtex-file, 4 PRB pages with 5 embedded eps figures. Hardcopies of figures (or the entire manuscript) may be obtained also by e-mail request to R.Eder@phys.rug.nlCondensed Mattertext