Strict site-occupation constraint in 2d Heisenberg models and dynamical mass generation in $QE{D}_3$ at finite temperature

We study the effect of site occupation in 2d quantum spin systems at finite temperature in a $\pi$-flux state description at the mean-field level. We impose each lattice site to be occupied by a single SU(2) spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a $QE{D}_3$ Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.