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.
The interplay of non-local Coulomb repulsion and Hund's coupling in the d-orbital manifold in frustrated triangular lattices is analyzed by a mutliband 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 AgNiO2. The potential relevance to other triangular transition …
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 …
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 i…
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 $\sqrt{12} \times \sqrt{12}$…
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 $μ_s$. The phase transition is found to be first order for $μ_s=0$, but becomes continuous with increasing $μ_s$. The particle and hole excitation spectra exhibit dramatic changes in the vicinity of…
Ground state properties of spinless, extended Falicov-Kimball model (FKM) on a finite size triangular lattice with orbital magnetic field normal to the lattice are studied using numerical diagonalization and Monte-Carlo simulation methods. We show that the ground state configurations of localized electrons strongly depend on the magnetic field. Magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered regular phase except at density $n_f = 1/2$ of localized electrons. It is proposed that magnetic field can be used as a new tool to produce segregated p…
We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion $V_2$ induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large $V_2$ by mean-field th…
A numerical diagonalization technique with canonical Monte-Carlo simulation algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a triangular lattice with correlated hopping ($t^{\prime}$). It is observed that the low temperature ordered phases (i.e. regular, bounded and segregated) persist up to a finite critical temperature ($T_{c}$). In addition, we observe that the critical temperature decreases with increasing the correlated hopping in regular and bounded phases whereas it increase…
We study the recently reported characteristic gapless charge ordered state in a spinless fermion system on a triangular lattice under strong inter-site Coulomb interactions. In this state the charges are spontaneously divided into solid and liquid component, and the former solid part aligns in a Wigner crystal manner while the latter moves among them like a pinball. We show that such charge ordered liquid is stable over a wide range of filling, $1/3<n<2/3$, and examine its filling dependent nature.
Correlated systems with hexagonal layered structures have come to fore with renewed interest in Cobaltates, transition-metal dichalcogenides and GdI2. While superconductivity, unusual metal and possible exotic states (prevented from long range order by strong local fluctuations) appear to come from frustration and correlation working in tandem in such systems, they freeze at lower temperature to crystalline states. The underlying effective Hamiltonian in some of these systems is believed to be the Falicov-Kimball model and therefore, a thorough study of the ground state of this model and its e…
Motivated by the importance of non-collinear and non-coplanar magnetic phases in determining various electrical properties of magnetic materials, we investigate the phase diagrams of the extended Hubbard model on anisotropic triangular lattice. We make use of a mean-field scheme that treats collinear, non-collinear and non-coplanar phases on equal footing. In addition to the ferromagnetic and 120° antiferromagnetic phases, we find the four-sublattice flux, the 3Q non-coplanar and the non-collinear charge-ordered states to be stable at specific values of filling fraction $n$. Inter-site Coulomb…
We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability oc…
A study of spinless matter fermions coupled to a constrained $\mathbb{Z}_{2}$ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared to previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (…
Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (C_v) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f-electron en…
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 quasi-localized (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 spin-flip scattering of itinerant electrons o…
A gas of strongly interacting spinless p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or Kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degree model. We determine the orbital ordering on the Kagome lattice, and show how orbital wave fluctuations select ground states via the order by di…
In spin-charge coupled systems, geometrical frustration of underlying lattice structures can give rise to nontrivial magnetic orders and electronic states. Here we explore such a possibility in the Kondo lattice model with classical localized spins on a triangular lattice by using a variational calculation and simulated annealing. We find that the system exhibits a four-sublattice collinear ferrimagnetic phase at 5/8 filling for a large Hund's-rule coupling. In this state, the system spontaneously differentiates into the up-spin kagome network and the isolated down-spin sites, which we call th…
Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied and compared with the results on a square lattice. Using a Falicov-Kimball model, the effects of the magnetic field, Coulomb correlation and finite system size on their energy spectrum are observed. It is possible to induce a gap in the spectrum by tuning the magnetic field even in the absence of correlation, though extra states appear in the gap due to finite size. An orbital current is calculated for both the square and triangular lattice with and without…
In this paper, we carry out a new technique named projection ED and indicate that it is applicable to the frustrated models, e.g., XXZ spin-1/2 Heisenberg and spinless fermion t-V models, in the strong coupling limit with highly degenerate ground states in a general way. As an example, we deal with a spinless fermion t-V model on a triangular lattice and show the usefulness of the method.
We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can…
We discuss the low-energy limit of three-orbital Kondo-lattice and Hubbard models describing $t_{2g}$ orbitals on a triangular lattice near half-filling. We analyze how very flat bands with non-trivial topological character, a Chern number C=1, arise both in the limit of infinite on-site interactions as well as in more realistic regimes. Exact diagonalization is then used to investigate fractional filling of an effective one-band spinless-fermion model including nearest-neighbor interaction $V$; it reveals signatures of fractional Chern insulators (FCIs) for several filling fractions. In addit…
Charge dynamics in an interacting fermionic model on a geometrically frustrated lattice are examined. We analyze a spinless fermion model on a paired triangular lattice, an electronic model for layered iron oxides, in zero and finite temperatures by the exact diagonalization methods. We focus on the two charge ordered (CO) phases, termed CO_1/2 and CO_1/3, which, respectively, are realized by the inter-site Coulomb interaction and the quantum/thermal fluctuations. The optical spectra in CO_1/3 show multiple components and their low-energy weights are survived even below the ordering temperatur…
We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a non-zero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions that is invariant under both time-reversal, $\mathbb{T}$, and a group of rotations and reflections, $\mathbb{G}$, which is either the dihedral point-symmetry group of an underlying lattice, $\mathbb{G}=D_n$, or the orthogonal group of rotations in continuum, $\mathbb{G}={\rm O}(2)$. Pairing symmetries are classified according to the irreducible representations…
Charge ordering (CO) with long-periodicities in a geometrically frustrated system, theta-(BEDT-TTF)2X, is numerically studied. We consider interacting fermion models on the anisotropic triangular lattice: the extended Hubbard model and the spinless fermion model, taking account of the inter-site Coulomb interactions on not only the nearest neighbor (NN) but also the next nearest neighbor (NNN) bonds. By applying Lanczos exact diagonalization method, we find that long-period charge correlations become dominant when NNN terms are included, in the charge-frustrated region. The calculated optical …
Superconducting and charge-ordered phases from Dirac quantum spin liquids on the triangular lattice
Center for Computational Quantum Physics, Flatiron Institute（Flatiron研究所计算量子物理中心）；Department of Physics, Harvard University（哈佛大学物理系）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
Lattice effects on photo-excited states in interacting charge frustrated system are examined. Real time dynamics in the interacting spinless fermion model on a triangular lattice coupled to lattice vibration are analyzed by applying the exact diagonalization method combined with the classical equation of motion. A photo-induced phase transition from the horizontal stripe-type charge order (CO) to the 3-fold CO occurs through a characteristic intermediate time domain. By analyzing the time evolution in detail, we find that this characteristic dynamics are seen when the electron and lattice sect…
We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repu…
Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 …
