Geometrical frustration effects on charge-driven quantum phase transitions

Abstract

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.

Combined Topological and Landau Order from Strong Correlations in Chern Bands

“…1(b). As has been discussed in the context of the pinball liquid [31][32][33]40], arXiv:1305.6948v2 [cond-mat.str-el] …”

Theories on Frustrated Electrons in Two-Dimensional Organic Solids

“…This question, not simple enough, is later on studied by Cano-Cortes et al [31] in the extended Hubbard model at 3/4-filling, which approximately correspond to taking U ∞ from the tV -results and allow the double occupancy of electrons. Before discussing this issue, we overview the earlier works on the same extended Hubbard model, which are summarized in the phase diagram in Figure 10(a); the results of the exact diagonalization by Merino et al [32], VMC by Watanabe et al [33], and DMRG with by Nishimoto et al [34] are put together for comparison.…”

“…The latest exact diagonalization study by Cano-Cortes et al [31,38] finally concluded that the above three-fold charge ordered metallic state is not necessarily identified as a pinball liquid. As found in their phase diagram in Figure 11(a), the three-fold charge ordered state at smaller U and large V , which is identical to the one in Figure 10(a), is transformed to a pinball liquid state at larger U .…”

Emergent lattices with geometrical frustration in doped extended Hubbard models

“…While these states are insulating, such exotic charge and magnetic orders become metallic away from the commensurate filling 4 . Furthermore, at quarter filling (n = 1/2), metallic states, named pinball liquids, have been also recently proposed [7][8][9][10] . They are characterized by a three-sublattice structure, in which the carriers of one sublattice are essentially localized (pins), with the remaining charges (balls) building an itinerant liquid on the interstitials.…”