Enhancing quantum order with fermions by increasing species degeneracy

One of the challenges for fermionic cold-atom experiments in optical lattices is to cool the systems to low enough temperature so that they can form quantum degenerate ordered phases. In particular, there has been significant work in trying to find the antiferromagnetic phase transition of the Hubbard model in three dimensions, without success. Here, we attack this problem from a different angle by enhancing the ordering temperature via an increase in the degeneracy of the atomic species trapped in the optical lattice. In addition to developing the general theory, we also discuss some potential systems where one might be able to achieve these results experimentally.

Figure 1

Comparison of the 2D DMFT (solid red line) and MC (blue dots, connected with a solid line as a guide to the eye) critical temperatures to the checkerboard density wave at half filling for both species on a square lattice with $N=1$. The lines marked as “Ising mean-field” (green) and “Ising exact” (black) show the critical temperatures for the corresponding Ising model, which become exact for the respective theories when $U\to \infty$.

Figure 2

The maximal critical temperature $T_c$ plotted as a function of mobile fermion degeneracy $N$ (as calculated with MC). The dashed line shows the corresponding DMFT $T_c$ calculated at $U=U_{\max }\left(\mathrm{DMFT}\right)$. The solid lines show MC $T_c$'s for different values of $U$. The black dotted line shows $T_c\left(\mathrm{DMFT}\right)\times 0.75$, which agrees well with nearly all the MC results. In the inset, $U_{\max }\left(\mathrm{DMFT}\right)$ is plotted as a function of degeneracy $N$, indicating it changes significantly with $N$.

Figure 3

The entropy of the mobile fermions $S_{\mathrm{mob}}\left(T_c\right)/N$ per mobile fermion at the critical temperature $T_c$ calculated in DMFT as a function of the mobile fermion degeneracy $N$.