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In this paper we reexamine the problem of the separation of spin and chargedegrees of freedom in two dimensional strongly correlated systems. We establisha set of sufficient conditions for the occurence of spin and charge separation.Specifically, we discuss this issue in the context of the Heisenberg model forspin-1/2 on a square lattice with nearest ($J_1$) and next-nearest ($J_2$)neighbor antiferromagnetic couplings. Our formulation makes explicit theexistence of a local SU(2) gauge symmetry once the spin-1/2 operators arereplaced by bound states of spinons. The mean-field theory for the spinons issolved numerically as a function of the ratio $J_2/J_1$ for the so-called s-RVBAnsatz. A second order phase transition exists into a novel flux state for$J_2/J_1>(J_2/J_1)_{{\rm cr}}$. We identify the range $0<J_2/J_1<(J_2/J_1)_{\rmcr}$ as the s-RVB phase. It is characterized by the existence of a finite gapto the elementary excitations (spinons) and the breakdown of all the continuousgauge symmetries. An effective continuum theory for the spinons and the gaugedegrees of freedom is constructed just below the onset of the flux phase. Weargue that this effective theory is consistent with the deconfinement of thespinons carrying the fundamental charge of the gauge group. We contrast thisresult with the study of the one dimensional quantum antiferromagnet within thesame approach. We show that in the one dimensional model, the spinons of thegauge picture are always confined and thus cannot be identified with thegapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.Comment: 56 pages, RevteX 3.

Separation of spin and charge quantum numbers in strongly correlated systems