Geometrical frustration effects on charge-driven quantum phase transitions

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 2kF 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)₂X, is discussed.