Finite-temperature phase transitions in the $\mathrm{SU}\left(N\right)$ Hubbard model

We investigate the $\mathrm{SU}\left(N\right)$ Hubbard model for the multicomponent 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 $N\le 6$ and find that low-temperature properties depend on the parity of the components. The magnetically ordered state competes with the correlated metallic state in the system with an even number of components $(N\ge 4)$, 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.

Figure 1

(a) AF state for $N=2$. (b) AF state for $N=4$. (c) CDW state for $N=3$. (d) CSAF state for $N=3$.

Figure 2

Order parameters $m$ as functions of the repulsive interaction $U/D$ when $T/D=0.02$. Lines are guides to the eye. The arrows indicate the existence of a hysteresis in the order parameters.

Figure 3

Phase diagrams for the multicomponent systems with $N=2,4,$ and 6. Solid squares represent the second-order magnetic phase transition points. Open (solid) circles represent the transition points, where the normal (AF) state disappears. Dashed lines represent the phase boundaries $N{D}^2/8(N-1)U$ obtained by means of the strong coupling expansion. Pluses (crosses) represent the transition points under the paramagnetic condition, where the metallic (Mott insulating) state disappears.

Figure 4

(a) Order parameter $m$ and (b) renormalization factor $z$ as functions of temperature for the four-component systems when $U/D=1.8,2.6$, and $5.0$.

Figure 5

Order parameters $m$ as functions of the repulsive interaction $U/D$ in the three-component system when $T/D=0.01,0.015$, and $0.02$.

Figure 6

Phase diagrams for the odd-component systems with $N=3$ and 5. Solid (open) circles indicate the state with (without) the order parameter for the $N=5$ system. The phase boundaries are guides to the eyes. The inset shows the temperature dependence of several quantities in the $N=3$ system with $U/D=8$ (see text).