U(N)/U(m)U(N-m) nonlinear sigma model: critical behavior and a physical realization

The nonlinear sigma model defined on the Grassmann manifold U(N)/U(m)U(N-m) is a direct generalization of the widely studied CP^N-1 model. In space dimension 2<d<4, we use 1/N expansion technique to obtain its critical exponents including two-particle ones, which are found to be only functions of m/N up to the first order. As a result, larger m effectively reduces N and thus brings stronger fluctuations. Next, we show such a model is a low energy description of the SU(N) Hubbard model which has been realized in cold atom experiments. With determinant quantum Monte Carlo simulations of the half-filled SU(6) Hubbard model on the square lattice, we have found strong evidences of a continuous quantum phase transition from the antiferromagnetic to valence bond solid states as U increases. Such a phase transition is described by the U(6)/U(3)U(3) nonlinear sigma model.