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

TL;DR

This paper investigates how imposing a strict site-occupation constraint affects the finite-temperature behavior of quantum Heisenberg-like spin systems, revealing significant quantitative differences from average constraint methods.

Contribution

It introduces a method to impose a strict site-occupation constraint and compares its effects on physical quantities and phase transition temperatures in quantum spin systems.

Findings

Transition temperatures are doubled with exact site-occupation compared to average methods.

Strict constraints significantly alter the behavior of physical quantities.

Comparison of spinon mass generation under different site-occupation constraints.

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 N\'eel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic N\'eel 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.