Spin and Charge Dynamics of thet−JModel

We investigate the dynamical spin and charge correlation functions, $S(\mathrm{Q}, \omega )$ and $N(\mathrm{Q}, \omega )$, for the two-dimensional (2D) $t-J$ model by using the exact diagonalization technique. Both quantities are compared with the 1D $t-J$ model. At high electron density ($n>\mathrm{}0.7\mathrm{}$), a remarkable feature emerges: $S(\mathrm{Q}, \omega )$ shows a pronounced peak at low energy of order $J$ which is consistent with $2k_F$ low-energy excitations, whereas low-energy $2k_F$-backscattering processes are strongly suppressed in the charge-density response. $N(\mathrm{Q}, \omega )$ consists of a dense and broad continuum, qualitatively different from the 1D charge response, implying strong interactions between charge and spin degrees of freedom.