Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs\(_2\)CuCl\(_4\) and to the layered organic superconductors \(\kappa\)-(BEDT-TTF)\(_2\)X

Abstract

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials \(\kappa\)-(BEDT-TTF)\(_2\)X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs\(_2\)CuCl\(_4\). We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite-N are also discussed. For parameters relevant to Cs\(_2\)CuCl\(_4\) the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator transition occurs at intermediate values of the interaction strength.