Magnetic Impurity in a Tonks Gas of Fermions

TL;DR

This paper proves that a magnetic impurity in a strongly interacting one-dimensional Fermi gas always induces a fully polarized ferromagnetic ground state, revealing novel magnetic behavior distinct from the Kondo effect.

Contribution

It provides a rigorous proof of ferromagnetism in a 1D strongly interacting Fermi gas with magnetic impurity, highlighting a cooperative mechanism different from traditional Kondo physics.

Findings

Ground state is always fully polarized ferromagnetic.

Spin gap increases linearly then decreases with magnetic coupling.

Ferromagnetism arises from avoiding frustration and large spin degeneracy.

Abstract

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.