Critical exponents of nonlinear sigma model on Grassmann manifold $U(N)/U(m)U(N-m)$ by $1/N$ expansion

Abstract

Motivated by the numerical evidence of a continuous phase transition between antiferromagnetic and paramagnetic phases in the half-filled SU(N) Hubbbard model, we studied its low energy nonlinear sigma model defined on Grassman manifold $U(N)/U(m)U(N-m)$ using the complex projective presentation, which is a direct generalization of the widely studied CP$^{N-1}$ model (corresponding to $m=1$). With the $1/N$ expansion technique up to the first order by fixing $m$ in space dimension $2<d<4$, we calculate the critical exponents of the Neel moment, which are found to be only functions of $m/N$. Our results indicate that larger $m$ effectively reduces $N$ and thus brings stronger fluctuations around the saddle point at $N=\infty$.