Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [T. A. Tóth et al., Phys. Rev. Lett. 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of $m=0.2\text{--}0.4$ in the thermodynamic limit.

Figure 1

Proposed three-sublattice order for the SU(3) Heisenberg model on the square and triangular lattice. The triangular lattice is obtained from the square lattice by adding couplings along the dashed bonds shown above. Blue boxes indicate the sites that are pinned to a specific flavor in our DMRG simulations in order to explicitly break SU(3) symmetry.

Figure 2

Comparison of the energy per site (upper panel) and the local moment (lower panel) of the SU(3) model (2) on the triangular lattice, obtained from LFWT, ED, DMRG, and iPEPS. In each plot, the DMRG results are shown as a function of the inverse system length $1/L$ (lower x axis), whereas the iPEPS results are shown as a function of inverse bond dimension $1/D$ (upper x axis). Dotted lines are only guides to the eye.

Figure 3

Bond energies and local color densities in the triangular $(7+2)\times 7$ lattice obtained from DMRG. The thickness of the bonds is proportional to the magnitude of the bond energy. An external potential is applied on the first and the last column to pin the sites to a specific color.

Figure 4

DMRG results with $D=4800$ states: Local moments as defined in Eq. (24) for the triangular (top panel) and square (bottom panel) lattice for a system size $(7+2)\times 7$. The plateau is very flat in the case of the square lattice, while corrections from the boundary are more pronounced for the triangular lattice.

Figure 5

Same plot as in Fig. 2 but for the SU(3) model (2) on the square lattice.

Figure 6

Bond energies and local color densities in the square $(7+2)\times 7$ lattice obtained from DMRG. The thickness of the bonds is proportional to the magnitude of the bond energy. An external potential is applied on the first and the last column to pin the sites to a specific color.