  In this paper we shall study a gauge theory of nodal spinons which appears as
a low-energy effective theory for antiferromagnetic (AF) Heisenberg models. In
most of studies on the nodal spinons given so far, the gauge interaction
between spinons was assumed weak and nonperturbative effects like instantons
and vortices were ignored. In the present paper, we shall study strong-coupling
gauge theory of nodal spinons and reveal its nontrivial phase structure. To
this end, we employ recently developed lattice gauge theory techniques for
studying finite-temperature and finite-density gauge theory. At low temperature
and low spinon-density region, an AF long-range order exists. As temperature
and/or density of spinons are increases, a phase transition to nonmagnetic
phase takes place. Order of the phase transition is of second (first) order for
low (high) density region of spinons. At a quantum critical point at vanishing
temperature T=0, abrupt change of spinon density occurs as a function of the
chemical potential. Implications of the results to the heavy-fermion materials
and the high-$T_c$ cuprates are discussed.
