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In this paper we shall study a gauge theory of nodal spinons which appears asa low-energy effective theory for antiferromagnetic (AF) Heisenberg models. Inmost of studies on the nodal spinons given so far, the gauge interactionbetween spinons was assumed weak and nonperturbative effects like instantonsand vortices were ignored. In the present paper, we shall study strong-couplinggauge theory of nodal spinons and reveal its nontrivial phase structure. Tothis end, we employ recently developed lattice gauge theory techniques forstudying finite-temperature and finite-density gauge theory. At low temperatureand low spinon-density region, an AF long-range order exists. As temperatureand/or density of spinons are increases, a phase transition to nonmagneticphase takes place. Order of the phase transition is of second (first) order forlow (high) density region of spinons. At a quantum critical point at vanishingtemperature T=0, abrupt change of spinon density occurs as a function of thechemical potential. Implications of the results to the heavy-fermion materialsand the high-$T_c$ cuprates are discussed.Comment: 15 pages and 6 figures, the version to appear in Mod.Phys.Lett.

STRONG-COUPLING GAUGE THEORY OF NODAL SPINONS AND ANTIFERROMAGNETIC LONG-RANGE ORDER