Abstract
A multicomponent anisotropic $t\ensuremath{-}J$ model with a hard-core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius $(\ensuremath{\Delta}+1)/2.$ The ground-state Bethe equations are analyzed and solved numerically for an arbitrary band filling, several values of color components, and the coupling constants. The ground-state energy, the Fermi velocity, and the critical exponents of the correlation functions have been calculated numerically for an arbitrary density of electrons. We discuss the effect of the hard-core potential. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. In comparison to the traditional anisotropic $t\ensuremath{-}J$ model in which $\ensuremath{\Delta}=0,$ the Fermi velocity is strongly enhanced in general. In the high-density limit, there is no dynamics of charges, the model exhibits a metal-insulator phase transition, and reduces to an antiferromagnetic spin chain with a new spacing parameter $\ensuremath{\Delta}+1.$
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