Exact charge dynamics in the supersymmetric t-J model with inverse-square interaction

The dynamical charge structure factor N(Q,ω) with Q smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with 1/r² interaction. Strong spin-charge separation in dynamics is found. N(Q,ω) with a given electron density does not depend on the spin polarization of a system with an arbitrary size. In the thermodynamic limit, only two holons and one antiholon contribute to N(Q,ω). These results together with generalized ones for the SU(K,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.