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arXiv:1510.08303

Magnetic Impurity in a Tonks Gas of Fermions

Deping Zhang, Wei Chen, Hui Zhai

Published Oct 28, 2015• 1 citation
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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.

DOI
10.48550/arxiv.1510.08303

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We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.
To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we introduce a model of ferromagnetic single-impurity Kondo problem in a multi-band one-dimensional δ-potential Fermi gas, which is exactly solvable for a special Kondo coupling constant via Bethe ansatz. It is found that the boundary potential modifies the local moment seriously due to the charge-spin coupling and the strong backward scattering off the impurity, and thus strongly affects the fixed point of the system. Generally, their is a residual entropy for the ground state which depends on the strength of the boundary potential. In addition, the tunneling effect through the impurity and the breakdown of the open boundary induced by the impurity are also discussed.
We investigate spin-charge separation of a spin-12\frac{1}{2}21​ Fermi system confined in a triple well where multiple bands are occupied. We assume that our finite fermionic system is close to fully spin polarized while being doped by a hole and an impurity fermion with opposite spin. Our setup involves ferromagnetic couplings among the particles in different bands, leading to the development of strong spin-transport correlations in an intermediate interaction regime. Interactions are then strong enough to lift the degeneracy among singlet and triplet spin configurations in the well of the spin impurity but not strong enough to prohibit hole-induced magnetic excitations to the singlet state. Despite the strong spin-hole correlations, the system exhibits spin-charge deconfinement allowing for long-range entanglement of the spatial and spin degrees of freedom.
Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-12\frac{1}{2}21​ honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases, respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite Z2{Z}_{2}Z2​ flux at the impurity site. For the antiferromagnetic case, this result has been obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is, however, nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that the weak-to-strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.
A recent experiment at the European Laboratory for Non-Linear Spectroscopy (LENS) on a three-dimensional (3D) Fermi gas has reported a negative effective mass (m∗<0{m}^{*}<0m∗<0) for Fermi polarons in the strongly repulsive regime. There naturally arises a question of whether the negative m∗{m}^{*}m∗ is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this paper, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in one dimension, which also can exhibit a negative m∗{m}^{*}m∗ in the super-Tonks-Girardeau regime. By analyzing the total spin, quasimomentum distribution, and pair correlations, we conclude that the negative m∗{m}^{*}m∗ is irrelevant to the instability towards ferromagnetism or phase separation but rather an intrinsic feature of collective excitations for fermions in the strongly repulsive regime. Surprisingly, for large and negative m∗{m}^{*}m∗, such an excitation is accompanied with a spin-density modulation when the majority fermions move closer to the impurity rather than being repelled far away, contrary to the picture of phase separation. These results shed light on the recent observation of negative m∗{m}^{*}m∗ in the 3D repulsive Fermi polarons.