Transition from band insulator to Mott insulator and formation of local moment in the half-filled ionic SU(N) Hubbard model

Abstract

We investigate the local moment formation in the half-filled $\mathrm{SU}(N$) Hubbard model under a staggered ionic potential. As the Hubbard $U$ increases, the charge fluctuations are suppressed and eventually frozen when $U$ is above a critical value ${U}_{c}$, marking the development of well-defined local moment with integer $m$ fermions on the A sublattice and $(N\ensuremath{-}m)$ fermions on the B sublattice, respectively. We obtain an analytical solution for ${U}_{c}$ for the paramagnetic ground state within the variational Gutzwiller approximation and renormalized mean field theory. For large $N$, ${U}_{c}$ is found to depend on $N$ linearly with fixed $m/N$, but sublinearly with fixed $m$. The local moment formation is accompanied by a peculiar phase transition from the band insulator to the Mott insulator, where the ionic potential and quasiparticle weight are renormalized to zero simultaneously. Inside the Mott phase, the low-energy physics is described by the $\mathrm{SU}(N$) Heisenberg model with conjugate representations, which is widely studied in the literature.