Connecting single-layer $t$-$J$ to Kondo lattice models: Exploration with cold atoms

Abstract

The Kondo effect, a hallmark of many-body physics, emerges from the antiferromagnetic coupling between localized spins and conduction fermions, leading to a correlated many-body singlet state. Here we propose to use the mixed-dimensional (mixD) bilayer Hubbard geometry as a platform to study Kondo lattice physics with current ultracold atom experiments. At experimentally feasible temperatures, we predict that key features of the Kondo effect can be observed, including formation of the Kondo cloud around a single impurity and the competition of singlet formation with Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for multiple impurities, summarized in the Doniach phase diagram. Moreover, we show that the mixD platform provides a natural bridge between the Doniach phase diagram of the Kondo lattice model, relevant to heavy-fermion materials, and the phase diagram of cuprate superconductors as described by a single-layer Zhang-Rice type $t$-$J$ model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.

Figures (10)

• Figure 1: a. Exploration of Kondo lattice (KL) physics (bottom) and single-layer $t$-$J$ models (top), within a single mixD bilayer setup. By implementing a strong potential gradient $\Delta$ between the impurity (upper) and conduction (lower) layer, a widely tunable Kondo interaction $J_K(\Delta)$ can be realized for cold atoms. b. For strong $J_K\gg t$, singlets form on each rung and effectively behave as dopants in the magnetic background of a single-layer model. c. For smaller $J_K$, the KL with its underlying competition between Kondo and RKKY physics can be explored, including in the experimentally feasible regime with on-site Hubbard interactions in both layers.
• Figure 2: Time evolution of the impurity density $\langle \hat{n}^I\rangle$, spin $\langle \hat{S}^{zI}\rangle$ and total spin-bath correlator $\langle \hat{\chi}\rangle$ after coupling to a bath of $L=20$ sites at time $\tau=0$ (see inset). Conduction baths with $U_c=U_I=8.0t_c$ (solid lines) and $U_c=0$ (dashed lines) are considered; in both cases $U_I=8.0t_c$, $\Delta=U_I/2$ and $n_c=0.7$. All calculations are for temperature $T=0$.
• Figure 3: RKKY vs. Kondo for two impurities coupled to a $t$-$J$ chain at finite temperatures $T$. a. The proposed setup, with impurity sites placed alternatingly below and above the conduction fermions to suppress direct couplings. b. Doniach phase diagram, with the RKKY (green) and Kondo (blue) regimes. c. Kondo signal $\langle \hat{\mathbf{S}}_{x_I}^I\cdot \hat{\mathbf{S}}_{x_I}^c\rangle$ (green) as well as the RKKY signal $\langle \hat{\mathbf{S}}_{x_{I_1}}^I\cdot \hat{\mathbf{S}}_{x_{I_2}}^I\rangle$ (blue and red), for different temperatures $k_BT$ and Kondo couplings $J_K$, with $J_c/t_c=0.5$, $J_I/t_c=0$ and length $L=20$. For the former, we average over two impurities with distance $d_I=13$; for the latter, we fix $x_{I_1}=4$ and consider different distances $d_I=x_{I_1}-x_{I_2}$. Dotted gray lines indicate $d_I^*$, where a sign change is expected from Eq. \ref{['eq:RKKY']} for a non-interacting bath.
• Figure S1: The mixed-dimensional (mixD) bilayer setup: The mixD setup realizing a Kondo model in 1D with one or multiple impurities, arranged alternatingly below and above the conduction chain to suppress direct nearest-neighbor impurity coupling. By implementing a strong gradient $\Delta$ between impurity and conduction sites a Kondo coupling with suppressed tunneling can be realized (for potential $\Delta>0$ realizing the Anderson impurity model). The impurities can be localized by shaping the potential landscape with a digital mirror device (DMD, orange).
• Figure S2: Dynamical singlet formation experiment: a. Two experimental realizations are possible: (i) The one proposed in the main text and Fig. \ref{['fig:FH']} (top), where a single spin up on the impurity site is prepared and then coupled to the bath at $\tau=0$. (ii) Alternatively, a singlet can be prepared and only one site is coupled to the bath (bottom). b. The dynamical singlet formation in both scenarios (light and dark green) leads to the same total spin-bath correlator $\langle \hat{\chi}(\tau)\rangle$, with the lines lying on top of each other. Conduction baths with $U_c=U_I=8.0t_c$ (light green) and $U_c=0$ (dark green) are considered; in both cases $U_I=8.0t_c$, $\Delta=U_I/2$ and $n_c=0.7$. All calculations are for temperature $T=0$.