Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators

TL;DR

The paper addresses subgap tunneling in a 1D Mott insulator with a boundary magnetic impurity, showing that spinon-Kondo screening generates a universal power-law suppression in the TDOS near the threshold $\Delta_d$, rather than a conventional Kondo resonance. The authors combine nonlinear Luttinger liquid theory with DMRG to derive and verify that the impurity-induced subgap TDOS follows $\rho_i(E) \propto (|E|-\Delta_d)^{-\alpha}$ with $\alpha=1-2(\gamma/\pi)^2$, and that at strong coupling $\gamma=\pi/2$ giving $\alpha=1/2$. In the strong-coupling picture, the electron fractionalizes into a holon bound state and a spinon vertex operator with scaling dimension $1/4$, producing a near-threshold $1/\sqrt{|E|-\Delta_d}$ singularity. These results yield clear STS signatures of spinon-Kondo physics in 1D and offer a pathway to probe spinon screening and related scaling in low-dimensional quantum magnets.

Abstract

We study the tunneling density of states (TDOS) in one-dimensional Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.

Figures (5)

• Figure 1: Schematic setup and TDOS near a boundary magnetic impurity in a 1D Mott insulator. (a) As example, we consider a half-filled Hubbard chain with on-site interaction strength $U>0$ and tunnel coupling $t_0$, connected by the coupling $t'$ to a boundary Anderson impurity with interaction $U_d>0$, see Eq. \ref{['model']}. We compute the TDOS $\rho_\sigma(j,E)$ in Eq. \ref{['tdos']}, which can be measured by STS via a probe tip, shown here at site $j=1$. (b) Boundary TDOS $\rho_{\rm b}(E)$ taken at $j=1$, where $\Delta$$\,(\Delta_d$) is the bulk (impurity) charge gap. The subgap resonance features for $\Delta_d<|E|<\Delta$ are power-law Fermi-edge singularities, see Eq. \ref{['subgapregime']}, where the power-law exponent $\alpha=1/2$ is caused by the spinon-Kondo effect. We here assume that $\Delta_d$ and $\Delta$ are well separated such that the subgap TDOS contribution becomes very small for $|E|\approx \Delta$. In that case, the linear TDOS energy dependence for $|E|>\Delta$ near the boundary is also observable in the presence of the magnetic impurity.
• Figure 2: At the strong-coupling fixed point (top), a spinon from the bulk screens the magnetic moment of the electron at the impurity site $j=0$. After applying $c_{0\uparrow}^\dagger$, the two electrons at $j=0$ form a singlet (bottom). As a consequence, the Kondo singlet is broken and a spinon is added to the chain boundary.
• Figure 3: DMRG results for the energy dependence of the TDOS at sites $j=0,1,2$ for the model \ref{['model']}, using $L=23$ with $t_0=1$, $U=10$, $U_d=3$, and $t'=0.6$. The Lorentzian broadening is $\eta=0.1$. The shaded region marks the continuum of bulk states with $E>\Delta$. We note that for each site $j$, the TDOS integrated over all energies gives the same value; note that here the curves for $j=1,2$ have been rescaled. The corresponding sum rule is discussed in the Appendix.
• Figure 4: Near-threshold behavior of the impurity TDOS for $\eta=0.075$. Other parameters are as in Fig. \ref{['fig3']}, where differences can be traced back to the different values for $\eta$. (a) Data points represent DMRG results for $\rho_{\rm i}(E)$ for several $t'$. Solid lines are fits to Eq. (\ref{['fitformula']}) with $A$, $\Delta_d$, and $\alpha$ as fitting parameters. (b) Power-law exponent $\alpha$ vs $t'$ obtained from the fits. The dashed line shows $\alpha=1/2$ as predicted by field theory.
• Figure 5: Integrated spectral weight $I_j$ of the subgap feature vs site index $j$ obtained from DMRG simulations for $L=23$ with $t_0=1$, $t'=0.6$, $U=10$, $U_d=3$, and $\eta=0.025$. Note the semi-logarithmic axes. The dashed curve is a guide to the eye only.