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arXiv:0805.0235 · Physical Review Letters

Kondo Polarons in a One-Dimensional Fermi Gas

Austen Lamacraft

Published Nov 26, 2008• 16 citations
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Abstract

We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting "Kondo polaron" takes the universal form mu-->3variant Planck's over vF2/2pikB2T2, in sharp contrast to the spinless case where mu proportional variant T(-4).

DOI
10.1103/physrevlett.101.225301

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We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting "Kondo polaron" takes the universal form mu-->3variant Planck's over vF2/2pikB2T2, in sharp contrast to the spinless case where mu proportional variant T(-4).
For a mobile spin-1/2 impurity, coupled antiferromagnetically to a one-dimensional gas of fermions, perturbative ideas have been used to argue in favor of two-channel Kondo behavior of the impurity spin. Here we combine general considerations and extensive numerical simulations to show that the problem displays a novel quantum phase transition between two-channel and one-channel Kondo screening upon increasing the Kondo coupling. We construct a ground-state phase diagram and discuss the various nontrivial crossovers as well as possible experimental realizations.
We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.
We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.
We study the low-temperature thermodynamics of a spin-SSS magnetic impurity coupled to m> 2m>~2m> 2 degenerate bands of interacting electrons in one dimension. By exploiting boundary-conformal-field-theory techniques, we derive exact results for the possible impurity thermal and magnetic response. The leading behavior of the impurity magnetic susceptibility is shown to be insensitive to the electron-electron interaction. In contrast, there are two types of scaling behavior of the impurity specific heat consistent with the symmetries of the problem: Either it remains the same as for the ordinary multichannel Kondo problem for noninteracting electrons or it acquires a new leading term governed by a critical exponent ${\ensuremath{\alpha}}_{m}{=(g}_{m}^{\ensuremath{-}1}\ensuremath{-}1)/m,$ where gm< 1{g}_{m}<~1gm​< 1 is a generalized (mmm channel) Luttinger-liquid charge parameter measuring the strength of the repulsive electron-electron interaction. We conjecture that the latter behavior is indeed realized when the impurity is exactly screened (m=2S).(m=2S).(m=2S).
We calculate the exact spectral function of a single impurity repulsively interacting with a bath of fermions in one-dimensional lattices, by deriving the explicit expression of the form factor for both regular Bethe states and the irregular spin-flip state and η-pairing state, based on the exactly solvable one-dimensional Hubbard model. While at low impurity momentum Q∼0 the spectral function is dominated by two power-law Fermi singularities, at large momentum we observe that the two singularities develop into two-sided distributions and eventually become anomalous Fermi singularities at the boundary of the Brillouin zone (i.e., Q=±π), with the power-law tails extending toward low energy. Near the quarter filling of the Fermi bath, we also find two broad polaron peaks at large impurity momentum, collectively contributed by many excited many-body states with non-negligible form factors. Our exact results of those distinct features in one-dimensional Fermi polarons, which have no correspondences in two and three dimensions, could be readily probed in cold-atom laboratories by trapping highly imbalanced two-component fermionic atoms into one-dimensional optical lattices.