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

TL;DR

This paper studies how increasing interaction strength in a half-filled ionic SU(N) Hubbard model causes a transition from a band insulator to a Mott insulator, leading to local moment formation and a phase transition characterized by renormalized parameters.

Contribution

It provides an analytical determination of the critical interaction strength for local moment formation and characterizes the phase transition in the SU(N) Hubbard model with ionic potential.

Findings

Critical U_c depends linearly on N for fixed m/N

Phase transition involves simultaneous renormalization of ionic potential and quasiparticle weight

Low energy physics in Mott phase described by SU(N) Heisenberg model

Abstract

We investigate the local moment formation in the half-filled 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 $(N-m)$ 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 SU($N$) Heisenberg model with conjugate representations, which is widely studied in the literature.