Effects of a strict site-occupation constraint in the description of quantum spin systems at finite temperature

Abstract

We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov \cite{Popov-88}. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the Néel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic Néel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a $QED_3$ Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.