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Magnetic Impurity in a Tonks Gas of Fermions

In this letter we consider a magnetic impurity in a one-dimensional spin-$1/2$ Fermi gas with infinitely strong repulsive interaction between fermions. We rigorously prove that, independent of whether the magnetic coupling between impurity and fermions is ferromagnetic or anti-ferromagnetic, the ground state is always a fully polarized ferromagnetic state for the itinerant fermions. This ferromagnetism can be understood as a cooperative effect of avoiding frustration of magnetic coupling during fermion hopping and the large spin degeneracy of a fermion Tonks gas. By numerically diagonalizing a finite size system, we show that the spin gap first increases linearly with magnetic coupling strength in the weak coupling regime, while decreases in the strong coupling regime. Our results show that a magnetic impurity in a strongly correlated gas can exhibit effect different from the Kondo effect as in a weakly correlated Fermi liquid.