Fine structure of the spectra of the Kondo lattice model: Two-site cellular dynamical mean-field theory study

We study the antiferromagnetic and paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half filling using the cellular dynamical mean-field theory (CDMFT) with the numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the nonlocal correlations increase the gap in both the antiferromagnetic and Kondo insulator phases and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.

Figure 1

Spin-averaged local spectral function for different values of the discretization parameter $\mathrm{\Lambda }$ for (a) the CDMFT and (b) DMFT.

Figure 2

Spin-resolved local spectral function for different $N_{\mathrm{keep}}$ (b) in the CDMFT and (b) in the DMFT.

Figure 3

Local spectral functions as $J$ is increased until a transition to a paramagnetic phase occurs.

Figure 4

Comparison of the CDMFT (top) and DMFT (bottom) results for $J/D=0.3$.

Figure 5

(a) $\mathbf{K}$-resolved spectral functions for $J/D=0.3$ (strong-coupling regime) within the CDMFT, with close-ups to the region around $(\pi ,\pi ,\pi )$ responsible for the spin resonances. (b) $\mathbf{K}$-resolved spectral function $A_{A\uparrow }\left(\omega ,{\epsilon }_{(k,k,k)}\right)$ for $J/D=0.3$ within the DMFT.

Figure 6

(a) Spectral function at constant $\mathbf{K}$ within the CDMFT and (b) constant ${\epsilon }_K$ within the DMFT for $J/D=0.3$.

Figure 7

Evolution of gap $\mathrm{\Delta }$ as $J$ is increased with DMFT (dashed line) and CDMFT (solid line) for cubic lattice.

Figure 8

(a) Sublattice magnetizations, (b) $f$ spin-spin correlations, and (c) $f$ spin-$c$ spin correlations as $J$ is increased with CDMFT for the cubic lattice. The operator $D\langle AB\rangle$ is the dynamic part of the correlation, i.e., $\langle AB\rangle -\langle A\rangle \langle B\rangle$.

Figure 9

Double occupancy and the same spin occupancy for the itinerant band ($c$) electrons on neighboring sites on the cubic lattice as a function of $J$.

Figure 10

Fit to ansatz (20) for CDMFT (solid lines) and DMFT (dashed lines) self-energies on the cubic lattice.