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.
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.
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 existence of three-sublattice long-range order is confirmed by the finite-size scaling analysis of the charge structural factor at V_c/t > 12. This 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. The Fermi surface is reconstructed at V=V_c and remains towards the strong coupling limit. These features reminiscent of the strong correlation together with the large value of V_c/t distinguishes the pinball liquid from the conventional charge-density-wave.
We study ground state properties and particle excitation spectra across a commensurate charge density wave transition in a system of strongly interacting fermions, using series expansion methods and mean-field theory. We consider a 1/3-filled system of spinless fermions on a triangular lattice, with hopping parameter t, nearest-neighbor repulsion V, and a sublattice dependent chemical potential ${\ensuremath{\mu}}_{s}$. The phase transition is found to be first order for ${\ensuremath{\mu}}_{s}=0$, but becomes continuous with increasing ${\ensuremath{\mu}}_{s}$. The particle and hole excitation spectra exhibit dramatic changes in the vicinity of the phase transitions and in the charge density wave ordered phase. We discuss the relevance of this study to the pinball Fermi liquid phase postulated theoretically in earlier studies as well as to various strongly correlated triangular lattice materials.
Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly-correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive onsite and nearest-neighbor interaction, arbitrary charge concentration, and 3×3 supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify 8 charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.
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 ${t}^{\ensuremath{'}}/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ 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.
Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (t being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For U>Uc2, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For Uc1<U<Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.