Pinball Liquid Research Articles

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio $t'/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12} \times \sqrt{12}$ droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

Pinball liquid phase from Hund's coupling in frustrated transition-metal oxides

The interplay of nonlocal Coulomb repulsion and Hund's coupling in the $d$-orbital manifold in frustrated triangular lattices is analyzed by a multiband extended Hubbard model. We find a rich phase diagram with several competing phases, including a robust pinball liquid phase, which is an unconventional metal characterized by threefold charge order, bad metallic behavior, and the emergence of high-spin local moments. Our results naturally explain the anomalous charge-ordered metallic state observed in the triangular layered compound ${\mathrm{AgNiO}}_{2}$. The potential relevance to other triangular transition-metal oxides is discussed.

Frustrated electrons on a spatially anisotropic triangular lattice: Emergent competition of charge orders and exotic disorders due to thermal fluctuations

We study the interplay of correlation and thermal fluctuation in a system consisting of two species of classical particles with up and down spin on a geometrically frustrated anisotropic triangular lattice, described by an extended four-state Potts model. The model corresponds to the strong coupling limit of the extended Hubbard model at quarter-filling, which is known to host several competing charge ordered phases as well as an exotic quantum state called pinball liquid. The frustrated intersite Coulomb interactions together with the on-site Coulomb interaction generate macroscopically degenerate manifolds of low-energy states. They compete entropically at finite temperature and two characteristic states emerge; a threefold periodic charge ordered state and a quasi-one-dimensionally disordered state called ``good defect state'' characterized by the systematic generation of ferroelectric bonds. The two states show good correspondence with the threefold charge order and the pinball liquid in the extended Hubbard model, and are separated by the partial Mott transition taking place on one of the three sublattices of the triangular lattice.

Emergent Heavy Fermion Behavior at the Wigner-Mott Transition

We study charge ordering driven by Coulomb interactions on triangular lattices relevant to the Wigner-Mott transition in two dimensions. Dynamical mean-field theory reveals the pinball liquid phase, a charge ordered metallic phase containing quasilocalized (pins) coexisting with itinerant (balls) electrons. Based on an effective periodic Anderson model for this phase, we find an antiferromagnetic Kondo coupling between pins and balls and strong quasiparticle renormalization. Non-Fermi liquid behavior can occur in such charge ordered systems due to the spin-flip scattering of itinerant electrons off the pins in analogy with heavy fermion compounds.

Valence bond crystal and possible orbital pinball liquid in at2gorbital model

We study a model for orbitally degenerate Mott insulators, where localized electrons possess t_2g degrees of freedom coupled by several, competing, exchange mechanisms. We provide evidence for two distinct strongly fluctuating regimes, depending on whether superexchange or direct exchange mechanism predominates. In the superexchange-dominated regime, the ground state is dimerized, with nearest neighbor orbital singlets covering the lattice. By deriving an effective quantum dimer model and analyzing it numerically, we characterize this dimerized phase as a valence bond crystal stabilized by singlet resonances within a large unit cell. In the opposite regime, with predominant direct exchange, the combined analysis of the original model and another effective model adapted to the local constraints, shows that subleading perturbations select a highly resonating ground state, with coexisting diagonal and off-diagonal long-range orbital orders.

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 three-fold 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-CDW instability competes with the Coulomb driven three-fold charge order transition. The relevance of our results to the family of quarter-filled materials: theta-(BEDT-TTF)2X is discussed.

Momentum distributions of a spinless fermion t-V model on a triangular lattice in the strong coupling region

Spinless fermion t-V model on a triangular lattice has been studied. In the model, the presence of a novel metallic charge-ordered ground state named a pinball liquid state has been proposed. To clarify the metallic features in the pinball state, we calculate the momentum distribution function of the model. For comparison, we also analyze a corresponding model where charge ordering is strongly pinned. The results are consistent with the picture expected for the pinball liquid, where an insulating ordered state (pin) and a metallic state on the honeycomb lattice (ball) coexist.

Variational Monte Carlo Study of a Spinless Fermion t–V Model on a Triangular Lattice: Formation of a Pinball Liquid

We analyze a model of spinless fermions on a triangular lattice at half-filling interacting via strong nearest-neighbor repulsive interactions, V , using the variational Monte Carlo simulation technique. The comparative analysis of two different types of variational wave functions with and without translational symmetry breaking reveals that the system undergoes a phase transition at \(V_{\text{c}}/t \gtrsim 12\), accompanied by the reconstruction of the Fermi surface. The existence of three-sublattice long-range order in the strong coupling region is confirmed by the finite-size scaling analysis. The ordered phase shows characteristics expected for a so called “pinball liquid” state, which has the spontaneous separation of fermionic degrees of freedom into coexisting Wigner crystal-like charge order (pin) and a metal (ball). The pins are fixed in order to maximize the kinetic energy gain of balls which move almost freely. We also find the charge-density-wave-like state only for the symmetry broken wave functions at V < V c , which, however, possibly remains as a short-range order in the bulk limit, and is distinguished from the pinball liquid characterized by the large value of V c / t .

Strong coupling theory of the spinless charges on triangular lattices: Possible formation of a gapless charge-ordered liquid

We propose a new type of charge liquid state in the spinless fermion system on a triangular lattice under strong inter-site Coulomb interactions, $V$. In the strong coupling limit ($t=0$), the ground state is classical and disordered due to geometrical frustration. The introduction of small t will drive the system to a partially ordered phase which we call a "pinball liquid". A possibly long range ordered Wigner crystal solid coexist with a liquid component which are moving around them like a pinball. This liquid is dominant over wide range of filling, even away from the regular triangle, and is also realized in the hard core boson systems. Relevance to the organic theta-ET_2X is discsussed.

Phase Diagram of Spinless Fermions on an Anisotropic Triangular Lattice at Half-filling

The strong coupling phase diagram of the spinless fermions on the anisotropic triangular lattice at half-filling is presented. The geometry of inter-site Coulomb interactions rules the phase diagram. Unconventional charge ordered phases are detected which are the recently reported pinball liquid and the striped chains. Both are induced by the quantum dynamics out of classical disordered states and afford extremely correlated metallic states and the particular domain wall-type of excitations, respectively. The disorder once killed by the quantum effect revives at the finite temperature, which is discussed in the terms of the organic $\theta$-ET$_2X$.