Mott transition in the one-dimensional SU$\left(n\right)$ Hubbard model

The one-dimensional SU$\left(n\right)$ Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for $n>2$. It is found that in the half-filled case, the umklapp processes couple the spin and charge degrees of freedom and generate a finite gap for arbitrary finite positive $U$. This behavior is thus different from that at $1∕n$ filling, where there is one particle per site, in which case the dynamics of the two degrees of freedom can be separated and a critical $U_{\mathrm{c}}$ is needed for the Mott transition.

Figure 1

The four types of scattering processes and their respective coupling constants. The processes with couplings $g_1$ and $g_3$ correspond to large-momentum transfer processes (backward scattering and umklapp processes, respectively); in the $g_2$ and $g_4$ processes the momentum transfer is small (forward scattering).

Figure 2

The scaling curves in the leading logarithmic approximation. (a) Case $n=2$, (b) case $n=4$.

Figure 3

The scaling curves in the next-to-leading logarithmic approximation. (a) Case $n=2$, (b) case $n=4$.

Figure 4

The scaling curves for the half-filled model in the leading logarithmic approximation for three values of $\tilde{U}$.