Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices

Two-channel Kondo lattice serves as a model for a growing family of heavy-fermion compounds. We employ a dynamical large-$N$ technique and go beyond the independent bath approximation to study this model both numerically and analytically using renormalization group ideas. We show that the Kondo effect induces dynamic magnetic correlations that lead to an emergent spinon dispersion. Furthermore, we develop a quantitative framework that interpolates between infinite dimension where the channel-symmetry broken results of mean-field theory are confirmed, and one-dimension where the channel symmetry is restored and a critical fractionalized mode is found.

Figure 1

(a) The 1D version of the two-channel Kondo lattice model studied here. (b) The strong coupling leads to a channel magnet; two different patterns of channel symmetry breaking, channel FM (top) and channel AFM (bottom). Bold lines represent spin singlets. (c) The entropy $S$ of two-channel Kondo impurity vs channel asymmetry and temperature. At the symmetric point, $S$ reduces to a fraction of the high-$T$ value.

Figure 2

1D 2CKL model. The temperature evolution of (a) the effective energy ${ϵ}_{\mathrm{eff}}$ for spinons and (b) the inverse effective Kondo coupling $J_{K,\mathrm{eff}}^{-1}$ for holons. At high-$T$, $J_{K,\mathrm{eff}}=J_K$ with no $k$ dependence. Initially, Kondo effect develops locally and $J_{K,\mathrm{eff}}^{-1}\to 0$. Then dispersion emerges in both $G_{\chi }$ and $G_b$, with $J_{K,\mathrm{eff}}^{-1}$ vanishing only at $k\sim \pm k_F$ and ${ϵ}_{\mathrm{eff}}$ only at $k\sim 0$. Inset of (a): despite an $\mathrm{O}(1/N)$ RKKY interaction (black), an initial spinon dispersion (blue) can lead to an O(1) amplification to in the present overscreened case. Inset of (b): Entropy $S$ vs $T$ for 0D, 1D ($t_b=0.2t_c$), and $1{\mathrm{D}}^{\prime }$ ($t_b=0.0002t_c$).

Figure 3

The spectral function of (a) spinons and (b) holons in a 1D two-channel Kondo lattice at $T/J_K=0.0072$, showing emergent linearly dispersing spinons at $k=0$ (bare dispersion is quadratic) and holons with Fermi point at $\pm k_F$. Scaling collapse of spinon and holon Green’s functions in the 2CK critical regime in (c) 1D lattice ($z=2$) $0.0072\le T/J_K\le 0.03$ and (d) $\infty \mathrm{D}$ Bethe lattice ($z=\infty$) $0.006\le T/J_K\le 0.03$. For both cases, $J_K/t_c=6$, $t_b/t_c=0.2$, and $s=0.15$.

Figure 4

(a) The evolution of FS in the presence of small channel symmetry breaking in 1D and $\infty \mathrm{D}$ with temperature. (b) The scaling exponents ${\mathrm{\Delta }}_{b/\chi }$ in 1D from the numerics. The lines show the analytical values given by Eqs. (9).