Electron Addition Spectrum in the Supersymmetric $\mathit{t}-\mathit{J}$ Model with Inverse-Square Interaction

The electron addition spectrum $A^{+}(k,\omega )$ is obtained analytically for the one-dimensional (1D) supersymmetric $t-J$ model with ${1/r}^2$ interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of $A^{+}(k,\omega )$ has a simple analytic form with contributions from one spinon, one holon, and one antiholon—all of which obey fractional statistics. The upper edge of $A^{+}(k,\omega )$ in the $(k,\omega )$ plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.