From the condensed matter physics perspective, the most natural single orbital tight-binding Hamiltonians, and hence the most widely studied, contain two fermionic species, corresponding to spin-up and spin-down electrons. In cold atom systems, however, SU(N) symmetry, in which $N>2$ fermionic species reside within a single band, also occurs. To understand such experiments, the SU(N) Hubbard model has been increasingly studied. Here we present determinant quantum Monte Carlo simulations of the SU(N) Holstein Hamiltonian in which $N$ fermionic species couple to a single local phonon mode. We show that at half filling it has an insulating charge density wave phase (CDW) at low temperatures in which empty sites alternate with sites with $N$ particles. We determine the $N=3$ CDW phase diagram in the temperature $T$ versus electron-phonon coupling $\alpha$ plane at fixed phonon frequency ${\omega }_0$ and half filling $\rho =1.5$. The critical temperature $T_c$ for $N=3$ can be as high as two times the maximum attainable for $N=2$. We also obtain the $N$ dependence of $T_c$ for a representative, fixed, ${\omega }_0$ and $\alpha$.

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• Charge density waves
• Holstein model
• Lattice models in condensed matter
• Quantum Monte Carlo