Pathway to Kondo physics in ytterbium atom chains with repulsive spin impurities

Abstract

The Kondo effect is a paradigmatic model of strongly-correlated physics, where a magnetic impurity forms a many-body singlet with a fermionic environment. Cold gases of ytterbium (Yb) atoms have been proposed to be an ideal platform to study the Kondo effect since different internal states of the atom can be used to create both the impurity and the fermionic environment. In Yb gases, however, the atomic impurity interacts with the fermionic environment both through magnetic and potential scattering. These two scattering mechanisms counteract one another, raising the question of how robust Kondo screening remains. Here, we show that potential scattering can quench the Kondo screening in one-dimensional Yb gases; yet, strikingly, Kondo physics survives this quench in well-defined regimes. Combining analytical renormalization-group theory for a Luttinger liquid with density matrix renormalization group (DMRG) simulations, we identify a transition from a strongly- to a weakly-entangled impurity as potential scattering is increased. The two approaches show excellent agreement concerning the stability of Kondo physics throughout the different parameter regimes considered. Our results provide a quantitative criterion for the emergence of Kondo screening in one-dimensional Yb gases and delineate experimentally accessible regimes for its realization in cold-atom platforms.

Figures (7)

• Figure 1: Kondo physics in Yb atoms. (a) The level structure in Yb atoms exhibits a narrow clock transition between the electronic states $^1{\bf S}_0$ and $^3{\bf P}_0$ (marked by horizontal lines), pertaining to spin-1/2 (arrows) fermionic levels. Atoms in these states are labeled as the ground band, $|g\rangle$, and the excited band, $|e\rangle$, respectively. State selective trapping potentials (cosine vs. parabola) lead to mobile atoms in the ground band, while atoms in the excited band are localized by a strong confining potential. The resulting effective model [cf. Eq. \ref{['eq:Microscopic_Lattice_Model']}] is an impurity in a fermionic environment of spin-1/2 fermions interacting with (b) antiferromagnetic and (c) potential interactions. These interactions tend to draw atoms (b) towards or (c) away from the impurity. The dashed lines schematically represent the modulus of the wavefunction of atoms near the impurity site when either magnetic or potential scatterings are dominant.
• Figure 2: Phase diagram for the Kondo effect in the weakly interacting limit. We set $\tilde{J}(0) = 10^{-4}.$ The potential scattering is set to be: (a)--(b)$\tilde{V}(0)/\tilde{J}(0) = 0$ and (c) $\tilde{V}(0)/\tilde{J}(0) = 5$. (a) Corresponds to the RG flow of the ideal Kondo problem, (b) to the ideal Kondo problem with the leading irrelevant perturbations, and (c) the full RG flow including both potential scattering and the leading irrelevant interactions [cf. Eqs. \ref{['eq:RG_equations_final']}]. (I) Red marks the Kondo regime, (II) yellow the perturbative regime, and (III) purple the strong potential scattering regime dominated. The silver (black) dashed lines denote where the scaling dimensions of the magnetic interactions (potential scattering) are marginal. White $\mathbf{\cdot},{\star},{ \times},{ +}$ markers indicate the points considered in panels (i)-(iv) of Fig. \ref{['fig:5']}, respectively.
• Figure 3: Kondo temperature scaling. (a) Kondo temperature for various potential scattering strengths. The initial value of the magnetic scattering is $\tilde{J}(0)=10^{-3}$, and the maximum allowed initial potential scattering is $\tilde{V}(0)=10^{-2}$. In the inset, we plot the RG flows obtained from solving Eq. \ref{['eq:RG_equations_final']} for the magnetic interactions. The color scheme is the same as in Fig. \ref{['fig:7']} below, where thin lines denote the results for $\tilde{V}(0)/\tilde{J}(0)=100$, while thick transparent lines are for $\tilde{V}(0)=0$. We use dashed alternating thick lines when results overlap and would otherwise be indistinguishable. The Kondo temperature in the presence (absence) impurity scattering is denoted by $T_k^{(0)}$. The Kondo temperature is defined when the magnetic interactions are equal to unity: $\tilde{J}=1$.
• Figure 4: Luttinger liquid parameters. We calcuate the $K_\mu$ parameters, cf. Eqs. \ref{['eq:Krho']}-\ref{['eq:Ksigma']}, of the Fermi-Hubbard model \ref{['eq:Microscopic_Lattice_Model']} with DMRG. We consider a system of $L = 41$ sites with open boundary conditions, and set the MPS bond dimension $D=200$, cutoff $10^{-12}$ and perform a DMRG calculation with 100 sweeps. $N/L$ denotes the filling fraction of the chain.
• Figure 5: DMRG results of impurity–LL hybridization and screening mechanisms. We present results for (a) von Neumann entropy of the Yb impurity, cf. Eq. \ref{['eq:von_neumann_entropy']}, and (b) the chain screening correlator, cf. Eq. \ref{['eq:screening_correlator']}. The chosen parameters correspond to the white markers shown in Fig. \ref{['fig:4']}, (i) for the $\mathbf{\cdot}$ marker $(K_\rho,K_\sigma) \approx (0.71,1.04)$, (ii) for the ${\star}$ marker $(K_\rho,K_\sigma) \approx (1.03, 0.88)$, (iii) for the ${ \times}$ marker $(K_\rho,K_\sigma) \approx (0.94, 0.67)$, and (iv) for the ${ +}$ marker $(K_\rho,K_\sigma) \approx (1.33, 0.38)$. These LL parameters correspond to the following filling fractions $N/L$, and Fermi-Hubbard Interactions $U/t$: (i) $(N/L,U/t) = (20/41, 1.75)$, (ii) $(N/L,U/t) = (15/41, -0.45)$, (iii) $(N/L,U/t) = (14/41, -0.9)$, (iv) $(N/L,U/t) = (13/41, -1.75)$. We also set chain length of $L=41$ atoms with open boundary conditions, MPS bond dimension $D=500$, cutoff $10^{-12}$, and perform a DMRG calculation with $100$ sweeps. In (b) regions colored purple denote where the screening cloud is anti-aligned to the impurity, while regions colored teal are where the screening cloud is aligned with the impurity. We take the parameter regimes with both (a) large entanglement entropy and (b) an anti-aligned screening cloud as signatures of the Kondo effect.