Quantum Phases in Two-dimensional Frustrated Spin-1/2 Antiferromagnets

Investigating various spin-1/2 systems in two dimensions (2d), by means of exact diagonalization (ED) on small samples of N spins, we have found, up to now, four kinds of antiferromagnetic phases at T=0. Two of them display long range order (LRO): Néel or Valence Bond Crystal (VBC) LRO. The others are two different Spin-Liquids. The Néel case may be qualified as semi-classical: it is a groundstate of the (spin-∞) classical model with an order parameter reduced by quantum fluctuations. The others are purely quantum phases. The hamiltonians considered are SU(2) invariant, like the Heisenberg hamiltonian and its generalizations as the J1 − J2 model or the J1 − J2 − J3 model and the multiple-spin exchange (MSE) model. All these models of magnetism picture exchange (or super-exchange) between fermions. The permutation operator of two spins reads: