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Strong-Coupling Gauge Theory of Nodal Spinons and Antiferromagnetic Phase Transitions

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.