Spin and charge dynamics of the t-J model at intermediate electron densities: absence of spin-charge separation

We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D t-J model for intermediate and low electron densities, rho<0.7. Both correlation functions agree remarkably well with the convolution of the single-particle spectral function, i.e. the simplest estimate within the Fermi liquid picture. Deviations from the convolution are shown to originate from symmetry-related selection rules, which are unaccounted for in the convolution estimate. Comparing the momentum distribution in the final states of the low lying spin and charge excitations to that of the ground state we establish that for all fillings under consideration the low energy peaks in both correlation functions originate from particle-hole excitations, as expected in a Fermi liquid.