Abstract
A large N expansion technique, based on symplectic (Sp(N)) symmetry, for frustrated magnetic systems is studied. The phase diagram of a square lattice, spin S, quantum antiferromagnet with first, second and third neighbor antiferromagnetic coupling (the J1-J2-J3 model) is determined in the large-N limit and consequences of fluctuations at finite N for the quantum disordered phases are discussed. In addition to phases with long range magnetic order, two classes of disordered phases are found: (i) states similar to those in unfrustrated systems with commensurate, collinear spin correlations, confinement of spinons, and spin-Peierls or valence-bond-solid order controlled by the value of 2S (mod 4) or 2S (mod 2) ; (ii) states with incommensurate, coplanar spin correlations, and unconfined bosonic spin-1/2 spinon excitations. The occurrence of “order from disorder” at large S is discussed. Neither chirally ordered nor spin nematic states are found. Initial results on superconductivity in the t—J model at N=∞ and zero temperature are also presented.
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