One-dimensional two-orbital SU($N$) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

We investigate the zero-temperature phase diagram of two-orbital $\mathrm{SU}(N$) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the $\mathrm{SU}(N$) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the $N=2$ case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of $2N$ fermions.

Figure 1

Numerical phase diagram of the $p$-band model (4) obtained from the one-loop RG analysis in the $N=4$ case. The same phase diagram is obtained for all $N>4$ with a weak-$N$ dependence for the position of some phase-transition lines when $U_1>0$. For $N=3$, the vicinity of the harmonic line is hard to resolve numerically.

Figure 2

Numerical one-loop RG phase diagram for the $g-e$ model (1) with $t_g=t_e$ and $U_{gg}=U_{ee}$ in the $N=4$ case. The same phase diagram is obtained for all $N>4$ with a weak-$N$ dependence for the position of the phase-transition lines. For $N=3$, the latter are hard to be resolved numerically.

Figure 3

Phase diagram of the $p$-band model (4) for $N>2$. Same caption as Fig. 1. All phases are gapless with central charge $c=1$ and the dominant instabilities are indicated together with the competing MS one.

Figure 4

Phase diagram for the $g-e$ model (1) with $t_g=t_e$ and $U_{gg}=U_{ee}$ for $N>2$. Same caption as Fig. 2.