Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4 and to the layered organic superconductors kappa-(BEDT-TTF)(2)X (BEDT-TTF bis(ethylene-dithio)tetrathiafulvalene); X anion)

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the an isotropic triangular lattice in the large-N limit. These two models may des cribe respectively the magnetic and electronic properties of the family of layered organic materials K-(BEDT-TTF)(2)X, The Heisenberg model is also re levant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diag rams for each model. The Sp(N) :antiferromagnet is shown to have five diffe rent phases as a function of the size of the spin and the degree of anisotr opy of the triangular lattice. The effects of fluctuations at finite N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase wi th deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard -Heisenberg model exhibits an insulating dimer phase, an insulating box pha se, a semi-metallic staggered flux phase (SFP), and a metallic uniform phas e. The uniform and SFP phases exhibit a pseudogap, A metal-insulator transi tion occurs at intermediate values of the interaction strength.