Nonlocal Kondo effect and quantum critical phase in heavy-fermion metals

Heavy-fermion metals typically exhibit an unconventional quantum critical point or quantum critical phase at zero temperature due to the competition of the Kondo effect and magnetism. Previous theories were often based on certain local types of assumptions, and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice, and we introduce the concept of a nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations but a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in $\mathrm{Yb}{\mathrm{Rh}}_2{\mathrm{Si}}_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy-fermion quantum criticality.

Figure 1

(a) Illustration of the Kondo-Heisenberg model with independent electron baths where holons are not allowed to propagate on the lattice (left) and a shared bath in this work (right). (b) Theoretical phase diagram in the large-$N$ limit on the $\kappa$ and $T_K/J_H$ plane, showing four phases: the Néel state (AFM), the resonating valence bond (RVB) state, the heavy Fermi liquid (HFL), and the intermediate holon state (HS). The RVB state may turn into the valence bond solid (VBS) at finite $N$. The AFM and HFL phase boundaries are separated for small $\kappa$ but merge together for $\kappa \ge 0.47$. The intermediate HS region is missing under the local assumption (inset). The dashed line inside the HFL marks a transition from $\mathrm{\Delta }\ne 0$ (short-range magnetic correlations) to $\mathrm{\Delta }=0$ (a local Fermi liquid). The arrows indicate different routes of quantum phase transitions. (c) The Feynman diagram of nonlocal Kondo scattering mediated by propagating holons. (d) Experimental phase diagrams of CePdAl [3] and $\mathrm{Yb}{\left({\mathrm{Rh}}_{1-y}{\mathrm{Ir}}_y\right)}_2{\mathrm{Si}}_2$ [14]. The hatched area in the phase diagram of CePdAl marks the region with linear-in-$T$ resistivity. The arrows mark possible correspondences with those in (b).

Figure 2

(a) Holon (left panel) and spin (right panel) excitation spectra along the high-symmetry line of the Brillouin zone (inset) at $\kappa =0.1$ for $T_K/J_H=0.115$, 0.15, and 0.164 (from top to bottom) with different ground states as marked in (b). The color represents the intensity of the spectral functions $-C_{n_{\chi }}^{\prime \prime }(\mathbf{k},\omega )/\pi$ and $-C_S^{\prime \prime }(\mathbf{k},\omega )/\pi$. The spin spectra at $M$ are also plotted for clarity. (b) Evolution of the holon Fermi volume $V_{\text{FS}}^{\chi }$ as a function of $T_K/J_H$ at $\kappa =0.1$. (c) The spin spectral function at $\kappa =0.2$ and $T_K/J_H=0.2$ at a low, but finite, $T$ right above the AFM ground state. The white dashed lines are a guide to the eye.

Figure 3

Temperature dependence of (a) the inverse staggered susceptibility and (b) the specific heat coefficient at $\kappa =0.2$ for different values of $T_K/J_H$. The colors distinguish the AFM (blue), HS (red), and HFL (green) regions. The inset in (a) shows the power-law exponent $\alpha$ as a function of $T_K/J_H$ on the AFM side, and that in (b) compares the low-temperature spinon density of states in the HS and HFL regions. The arrows mark the gap edges. (c) and (d) Same as (a) and (b), but at $\kappa =0.48$, where the red color denotes the QCP.