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.

Typos corrected, one reference added. 20 pages, 17 figures, RevTeX 3.0

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• Large N expansion for frustrated and doped quantum antiferromagnets
• Quantum Phases of the Shastry-Sutherland Antiferromagnet
• Rung-Rung Current Correlations on a 2-Leg t-J Ladder
• Staggered Orbital Currents in a Model of Strongly Correlated Electrons

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