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Thomas C. Lang (1), Zi Yang Meng (2), Stefan Wessel (2), Fakher F. Assaad (1), 1 Universitaet Wuerzburg, 2 Universitaet Stuttgart We investigate the phase diagram of the half-filled $SU(N)$ Hubbard-Heisenberg model on the hexagonal lattice in the self-adjoint totally antisymmetric representation. By means of the projective ($T = 0$) quantum Monte Carlo method we simulate the model on lattices ranging up to ${L = 15}$ to study in detail the phase diagram as a function of $N$ in limit to the saddle point $N\rightarrow\infty$. For $U=0$ and in the limit of one-particle physics $N\rightarrow\infty$ the model shows a phase transition from semi-metal to a star-shape valence bond solid which is robust against fluctuations down to $N=6$. In the limit of full many body correlations, $N=2$, decreasing $t/J$ triggers a quantum phase transition from semi-metal to an antiferromagnetic-insulator with an apparent intermediate phase. At increased symmetry $N=4$ the Hubbard-Heisenberg model exhibits a paramagnetic spin- and quasiparticle gapped phase with no apparent order and unusual scaling behavior of correlations. |
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