Disorder-induced charge-density-wave–superfluid transition in $\mathrm{SU}\left(N\right)$ Fermi systems

We investigate $\mathrm{SU}\left(N\right)$ attractive Fermi systems with disorder using a Bogoliubov-de Gennes method at zero temperature with particular focus on the SU(3) case. The charge correlation function, the distribution function of the superfluid (SF) order parameter, and the free energy are calculated for a two-dimensional square lattice system at half filling. From the disorder average of these quantities, we find that disorder triggers a transition from the charge-density-wave (CDW) phase to the SF phase; disorder suppresses the CDW order, making the SF state stable. This disorder-driven phase transition is of first order and is unique for SU(3) systems; it has not been observed for the disordered SU(2) systems studied so far. We elucidate the properties of the CDW-SF transition from the disorder-averaged density of states and the distribution function of the particle density and thus obtain the ground-state phase diagram. We also address the SU(4) case and find that the CDW state is driven directly to the Anderson localized state, but the SF phase is not stabilized. We argue what will be expected for generic $N$ cases.

Figure 1

Charge correlation function $C\left(r_i-r_j\right)$ as a function of $|r_i-r_j|$ for three different values of the disorder strength, $\Delta =0.2$, 0.4, and 0.8, from top to bottom. The attractive interaction is chosen as $U=0.8$.

Figure 2

Site-averaged SF order parameter as a function $\Delta$ for three different values of the attractive interaction strength: $U=0.6$ (red solid line with crosses), $U=0.8$ (blue dotted line with open squares), and $U=1$ (black broken line with open circles).

Figure 3

Distribution function of the local SF order parameter $\mathrm{P}\left({\Phi }_i^{ba}\right)$ for three different parameter regions where the CDW order does not exist.

Figure 4

Site-averaged density of states: the top three panels are for the CDW phase and the bottom panel is for the SF phase.

Figure 5

Histogram of the local particle density $P\left(n_i\right)$: CDW phase (top three panels) and SF phase (bottom panel) for four different values of disorder strength, $\Delta =0.0$, 0.2, 0.4, and 0.8, from top to bottom at fixed $U=0.8$.

Figure 6

Left panel: Distribution of effective disorder $P\left(\delta {\mu }_{ia}\right)$ for the particles with spin $a$. The red solid line (blue dotted line) corresponds to the $N=3$ case (the $N=2$ case). Right panel: $P\left(\delta {\mu }_{ia}\right)$ and $P\left(\delta {\mu }_{ic}\right)$ in the $N=3$ case. The red solid line shows $P\left(\delta {\mu }_{ia}\right)$ and the black broken line shows $P\left(\delta {\mu }_{ic}\right)$. Parameters are chosen as $U=0.8$, $\Delta =0.6$, and $n=1.5$ in both panels.

Figure 7

Ground-state phase diagram of the SU(3) attractive Hubbard model with disorder. The red solid line with circles denotes the CDW-SF transition point and the black dotted line with crosses shows the points where $F_{\mathrm{CDW}}=F_{\mathrm{SF}}$. The blue solid line with closed triangles represents the boundary between the SF phase and the Anderson localized phase. The red dashed line with open circles and the blue dashed line with open triangles are deduced via the argument discussed in the text.

Figure 8

Charge correlation function $C\left(r_i-r_j\right)$ in SU(4) systems as a function of $|r_i-r_j|$ for four different values of the disorder strength: $\Delta =0.2$, 0.4, 0.8, and 1.6, from top to bottom. We study the attractive interaction strength, $U=0.8$.

Figure 9

Ground-state phase diagram of the SU(4) attractive Hubbard model with disorder. The blue solid line with closed triangles denotes the transition between the CDW phase and the Anderson localized phase. The blue dotted line with open triangles is drawn in a manner similar to that used in Fig. 7.