Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study

We show that for the half-filled Kondo lattice model on the honeycomb lattice a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo simulations of the so-called composite fermion spectral function. Within a $U\left(1\right)$ gauge theory formulation of the Kondo model, it becomes apparent that a Higgs mechanism dictates the weight of the resonance in the spectral function. For the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole gives way to incoherent spectral weight but it remains well defined for the square lattice. Our result provides an explicit example where the magnetic transition and the breakdown of heavy quasiparticles are detached as observed in $\mathrm{Yb}{\left({\mathrm{Rh}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{Si}}_2$ [S. Friedemann et al., Nat. Phys. 5, 465 (2009)].

Figure 1

Ground-state phase diagram of the half-filled Kondo lattice model on the honeycomb and square lattices. On both lattices we observe a magnetic order-disorder transition denoted by a red circle and order parameter corresponding to $\langle \mathit{S}\rangle$. For the honeycomb lattice (a) we observe a breakdown of the heavy quasiparticle in the spin-density-wave (SDW) phase as indicated by the vanishing residue $Z_{\mathit{k}}^{\psi }$ of the pole at the $\mathrm{\Gamma }$ point in the composite fermion Green's function. For the square lattice (b) we observe only the order-disorder transition since, down to our lowest value $J_k/W=0.025, Z_{\mathit{k}}^{\psi }$ at the $M=(\pi ,\pi )$ point remains finite. All the values of $Z_{\mathit{k}}^{\psi }$ are extrapolated to the thermodynamic limit [27]. We use the mean-field notation $\langle b\rangle$ to track the magnitude of the residue.

Figure 2

Composite fermion spectral function $A_{\psi }(\mathit{k},\omega )$ along the $\mathrm{\Gamma }-K\text{−}M\text{−}\mathrm{\Gamma }$ path in momentum space with $\mathrm{\Gamma }=(0,0), K=(\frac{4\pi }{3},0)$, and $M=(\pi ,\frac{\pi }{\sqrt{3}})$ on the $L=18$ honeycomb KLM for representative values of $J_k/W$ corresponding to (a) Kondo, (b) and (c) $\text{Kondo}+\mathrm{SDW}$, and (d) SDW phases.

Figure 3

(a) Composite fermion Green's function $G_{\psi }(\mathit{k}=\mathrm{\Gamma },\tau )$ at $J_k/W=0.067$, and (b)–(d) the corresponding spectral function $A_{\psi }(\mathit{k},\omega )$ on the honeycomb KLM with different sizes $L$.

Figure 4

(a) Composite fermion Green's function $G_{\psi }(\mathit{k}=M,\tau )$, where $M=(\pi ,\pi )$, at $J_k/W=0.025$, and (b)–(d) the corresponding spectral function $A_{\psi }(\mathit{k},\omega )$ along the $\mathrm{\Gamma }\text{−}X\text{−}M\text{−}\mathrm{\Gamma }$ path, where $X=(\pi ,0)$, on the square KLM with different sizes $L$.

Figure 5

(a) Single-particle gap ${\mathrm{\Delta }}_{\text{qp}}\left(\mathit{k}\right)$ at the $\mathrm{\Gamma }$ and Dirac $K$ points and (b) the local spin-spin correlation function $S^{\text{cf}}$ as a function of $J_k/W$ on the honeycomb lattice. For comparison, we show in (c) ${\mathrm{\Delta }}_{\text{qp}}\left(\mathit{k}\right)$ at the $M$ point and (d) $S^{\text{cf}}$ on the square lattice. Dashed lines denote the respective magnetic order-disorder transitions. All quantities are representative of the thermodynamic limit [27].