The interplay of Coulomb repulsion and geometrical frustration on charge-driven quantum phase transitions is explored. The ground-state phase diagram of an extended Hubbard model on an anisotropic triangular lattice relevant to quarter-filled layered organic materials contains homogeneous metal, "pinball," and threefold charge ordered metallic phases. The stability of the pinball phase occurring for strong Coulomb repulsions is found to be strongly influenced by geometrical frustration. A comparison with a spinless model reproduces the transition from the homogeneous-metallic phase to a pinball liquid, which indicates that the spin correlations should play a much smaller role than the charge correlations in the metallic phase close to the charge-ordering transition. Spin degeneracy is, however, essential to describe the dependence of the system on geometrical frustration. Based on finite-temperature Lanczos diagonalization we find that the effective Fermi temperature scale T * of the homogeneous metal vanishes at the quantum phase transition to the ordered metallic phase driven by the Coulomb repulsion. Above this temperature scale "bad" metallic behavior is found which is robust against geometrical frustration in general. Quantum critical phenomena are not found whenever nesting of the Fermi surface is strong, possibly indicating a first-order transition instead. "Reentrant" behavior in the phase diagram is encountered whenever the 2k F charge-density wave instability competes with the Coulomb driven threefold charge order transition. The relevance of our results to the family of quarter-filled materials, θ-(BEDT-TTF) 2 X, is discussed.

We perform an extensive study of Sr_{3}Cr_{2}O_{7}, the n=2 member of the Ruddlesden-Popper Sr_{n+1}Cr_{n}O_{3n+1} system. An antiferromagnetic ordering is clearly visible in the magnetization and the specific heat, which yields a huge transition entropy, Rln(6). By neutron diffraction as a function of temperature we have determined the antiferromagnetic structure that coincides with the one obtained from density functional theory calculations. It is accompanied by anomalous asymmetric distortions of the CrO_{6} octahedra. Strong coupling and Lanczos calculations on a derived Kugel-Khomskii Hamiltonian yield a simultaneous orbital and moment ordering. Our results favor an exotic ordered phase of orbital singlets not originated by frustration.