We investigate the SU(N ) Hubbard model for the multi-component fermionic optical lattice system, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We obtain the finite temperature phase diagrams with N ≤ 6 and find that low temperature properties depends on the parity of the components. The magnetically ordered state competes with the correlated metallic state in the system with the even number of components (N ≥ 4), yielding the first-order phase transition. It is also clarified that, in the odd-component system, the ordered state is realized at relatively lower temperatures and the critical temperature is constant in the strong coupling limit.

We investigate finite temperature properties in the half-filled three-component (colors) fermion systems. It is clarified that a color density-wave (CDW) state is more stable than a color-selective "antiferromagnetic" (CSAF) state against thermal fluctuations. The reentrant behavior in the phase boundary for the CSAF state is found. We also address the maximum critical temperature of the translational symmetry breaking states in the multicomponent fermionic systems. I. INTRODUCTIONUltracold fermions have attracted much interest [1][2][3]. One of the interesting topics is the phase transition to the symmetry breaking states such as the superfluid and magnetically ordered states. The former has been observed in the optical lattice [4], and the BCS-BEC crossover has also been discussed [5][6][7][8][9]. On the other hand, the latter translational symmetry breaking state should be hard to be realized since intersite correlations are extremely small in optical lattice systems. Recently, it has been reported that two component fermions reach a very low temperature close to the Neel temperature ∼ 1.4T N [10], which should accelerate further theoretical and experimental investigations on the observations of the translational symmetry breaking state.Multicomponent fermion systems such as Li [11,12], Yb [13,14] and Sr [15,16], should be the possible candidates to observe the translational symmetry breaking states. Miyatake et al. have theoretically studied ground state properties in the three component fermion systems with anisotropic interactions to clarify the existence of translational symmetry breaking states [17]. However, the stability of these ordered state against thermal fluctuations has not been discussed systematically [18]. In particular, it is necessary to clarify whether or not these ordered states can be realized at accessible temperatures. In addition, it is desired to clarify the role of the multicomponents in realizing the translational symmetry breaking state at finite temperatures.Motivated by this, we consider the ultracold fermion systems with three components on the optical lattice. Combining dynamical mean-field theory (DMFT) [19][20][21] with the non-crossing approximation (NCA) [22][23][24], we discuss finite temperature properties in the system. We also study the translational symmetry breaking state in the system with N c = 2, 3, · · · , 6, where N c is the number of components of fermions. Then we demonstrate that the maximum critical temperature for the six-component system is about twice higher than that for the two-component system.The paper is organized as follows. In §II, we introduce the model Hamiltonian for the three component fermion systems on the optical lattice and briefly summarize our theoretical approach. In §III, we study how stable the

We investigate spontaneously symmetry breaking states in the attractive SU(N ) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When N > 2, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.