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

Motivated by the realization of SU(N) antiferromagnetism with the multirow representations in coldatom physics, we studied its low-energy nonlinear sigma model defined on the Grassmann manifold U(N)/U(m)U(N - m) using the complex projective presentation, which is a direct generalization of the widely studied CPN-1 model (corresponding to m = 1). Using the large-N expansion up to the first order of 1/N with fixed in, and in space dimension 2 < d < 4, we obtain the critical exponents, including in particular the gauge-independent exponents that are directly relevant for experimental measurements. These exponents are found to depend only on rn/N, indicating that a larger rn effectively reduces N and thus causes stronger fluctuations about the saddle point.