We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.
We discuss the metal–insulator transition of the spinless fermion model with nearest-neighbor repulsion on the Kagomé lattice at 1/3- and 2/3-filling. The system is analyzed by using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the system is described by ring exchange processes. In the intermediate-coupling regime, we find that the qualitative properties of the metal–insulator transition at 1/3- and 2/3-filling are totally different reflecting the difference in the band structure near the Fermi level.
Motivated by the recent discovery of metallic kagome lattice materials,
AV3Sb5 (A = K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group method. We identify a metal-insulator transition around $U\ensuremath{\sim}{U}_{c1}$ and four distinct phases as a function of
U/t on narrower cylinders, including a metallic phase at
U<Uc1, two insulating intermediate phases (a translational symmetry breaking phase at
Uc1<U<Uc2 and a quantum spin liquid phase at
Uc2<U<Uc3), and the kagome antiferromagnetic phase at
U>Uc3. We confirm that the translational symmetry breaking phase is robust for wider cylinders, while the quantum spin liquid phase is smoothly connected to the kagome antiferromagnetic phase with increasing the system width. Moreover, our numerical observations indicate a continuous metal-insulator transition at
Uc1 whose nature is consistent with Slater's transition scenario. The magnetic phase transition between two insulating intermediate phases at
Uc2 is first order. Our findings may provide insights into exotic kagome lattice materials.
We study the metal-insulator transition in the half-filled Hubbard model on a Kagome lattice using the variational cluster approximation. The strong coupling limit of the model corresponds to the
S=1/2 Kagome Heisenberg antiferromagnet, which is known to have a singlet ground state, although its detail is still debated. As the results of the cluster methods generally depend much on the choice of the unit cluster, we have chosen the clusters that are compatible with these singlet ground states in the strong coupling case found so far, which basically consist of even number of sites. It is found that the correlated electrons on the Kagome lattice have a strong tendency to form valence-bond structures, which are the resonation of electrons on a single bond or several bonds forming loops. The zero-temperature metal-insulator transition at some interaction strength is possibly driven by the formation of such short range valence bonds and shows a second order character, which is distinctive from the Brinkman-Rice scenario. The electrons on these valence bonds further localizes onto each site as the interaction increases, and the valence bonds of electrons finally turn into magnetic singlet bonds between localized
S=1/2 spins, which are consistent with the ground states of the Kagome antiferromagnet.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that in the half-filled band case the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition. Outside half-filling correlated hopping stabilizes the segregated phase in the ground-state, however, the nature of the ground-state remains qualitatively unchanged.
We study a model of strongly interacting spinless fermions and hard-core bosons on an anisotropic kagome lattice near 2/3-filling. Our main focus lies on the strongly anisotropic case in which the nearest–neighbor repulsions V and V ' are large compared to the hopping amplitudes | t | and | t '|. When t = t ' = 0, the system has a charge ordered insulating ground state where the charges align in striped configurations. Doping one electron or hole into the ground state yields an anisotropic metal at V ' > V , where the particle fractionalizes along the V '-bonds while propagates along the V -bonds in a one–body like manner. The sixth order ring exchange processes around the hexagonal unit of the lattice play a crucial role in forming a bound state of fractional charges.