Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models

The absence of the negative sign problem in quantum Monte Carlo simulations of spin and fermion systems has different origins. World-line based algorithms for spins require positivity of matrix elements whereas auxiliary field approaches for fermions depend on symmetries such as particle-hole symmetry. For negative-sign-free spin and fermionic systems, we show that one can formulate a negative-sign-free auxiliary field quantum Monte Carlo algorithm that allows Kondo coupling of fermions with the spins. Using this general approach, we study a half-filled Kondo lattice model on the honeycomb lattice with geometric frustration. In addition to the conventional Kondo insulator and antiferromagnetically ordered phases, we find a partial Kondo screened state where spins are selectively screened so as to alleviate frustration, and the lattice rotation symmetry is broken nematically.

Figure 1

Phase diagram with in-plane antiferromagnetic ($xy\text{−}\mathrm{AFM}$), out-of-plane partial Kondo screening ($z\text{−}\mathrm{PKS}$), spin-rotation symmetry breaking partial Kondo screening ($xyz\text{−}\mathrm{PKS}$), and Kondo insulator (KI) phases from QMC simulations at $T=0.025$. Diamonds indicate onset of long-range order; solid (open) symbols are critical values based on $L=6$ and 9 ($L=9$ and 12), (see text). Insets: Model and schematic local moment structure in each phase.

Figure 2

$J^K$ dependence of correlation ratios for (a) in-plane antiferromagnetic and (b) out-plane three-sublattice orders. Here, $J^z=0.16$ and $T=0.025$.

Figure 3

Probability distribution of (a) ${\mathit{M}}_l$ and (b) ${\mathit{M}}_A{\mathit{M}}_B^{*}$ for the $z\text{−}\mathrm{PKS}$ phase at $J^z=0.60$ and $J^K=1.5$; see text. Here, $T=0.025$ and $L=9$.

Figure 4

(a) Single-particle gap ${\mathrm{\Delta }}_{\text{sp}}$ at the Dirac point [44] and (b) free-energy derivative $\partial F/\partial J^K$. Here, $T=0.025$.